diff --git a/src/qcodes/instrument/sims/lakeshore_model336.yaml b/src/qcodes/instrument/sims/lakeshore_model336.yaml
index f04d3f22d6e..1e0277c31b1 100644
--- a/src/qcodes/instrument/sims/lakeshore_model336.yaml
+++ b/src/qcodes/instrument/sims/lakeshore_model336.yaml
@@ -53,6 +53,17 @@ devices:
         setter:
           q: "range A,\"{}\""
 
+      sensor_curve_number_A:
+        default: 42
+        getter:
+          q: "INCRV? A"
+          r: "{}"
+
+      curve_data_query_for_curve_42:
+        getter:
+          q: "CRVHDR? 42"
+          r: "DT-042,01110042,2,342.0,1"
+
 
       temperature_B:
         default: 100.0
@@ -96,7 +107,16 @@ devices:
         setter:
           q: "range A,\"{}\""
 
+      sensor_curve_number_B:
+        default: 41
+        getter:
+          q: "INCRV? B"
+          r: "{}"
 
+      curve_data_query_for_curve_41:
+        getter:
+          q: "CRVHDR? 41"
+          r: "DT-041,01110041,2,341.0,1"
 
       temperature_C:
         default: 100.0
@@ -140,7 +160,16 @@ devices:
         setter:
           q: "range A,\"{}\""
 
+      sensor_curve_number_C:
+        default: 40
+        getter:
+          q: "INCRV? C"
+          r: "{}"
 
+      curve_data_query_for_curve_40:
+        getter:
+          q: "CRVHDR? 40"
+          r: "DT-040,01110040,2,340.0,1"
 
       temperature_D:
         default: 100.0
@@ -184,6 +213,17 @@ devices:
         setter:
           q: "range A,\"{}\""
 
+      sensor_curve_number_D:
+        default: 39
+        getter:
+          q: "INCRV? D"
+          r: "{}"
+
+      curve_data_query_for_curve_39:
+        getter:
+          q: "CRVHDR? 39"
+          r: "DT-039,01110039,2,339.0,1"
+
 
 resources:
   GPIB::2::INSTR:
diff --git a/src/qcodes/instrument_drivers/Lakeshore/Lakeshore_model_336.py b/src/qcodes/instrument_drivers/Lakeshore/Lakeshore_model_336.py
index 32ec33a7a4b..e482d08ed87 100644
--- a/src/qcodes/instrument_drivers/Lakeshore/Lakeshore_model_336.py
+++ b/src/qcodes/instrument_drivers/Lakeshore/Lakeshore_model_336.py
@@ -1,7 +1,7 @@
 from typing import TYPE_CHECKING, ClassVar
 
 import qcodes.validators as vals
-from qcodes.parameters import Group, GroupParameter
+from qcodes.parameters import Group, GroupParameter, Parameter
 
 from .lakeshore_base import (
     LakeshoreBase,
@@ -203,6 +203,78 @@ def __init__(
             get_cmd=f"INTYPE? {self._channel}",
         )
 
+        # Parameters related to temperature calibration curve (CRVHDR)
+        self.curve_number: Parameter = self.add_parameter(
+            "curve_number",
+            get_cmd=f"INCRV? {self._channel}",
+            set_cmd=False,
+            get_parser=int,
+            label="Temperature calibration curve number",
+        )
+        """
+        Temperature calibration curve number that is selected now
+        """
+        self.curve_name: GroupParameter = self.add_parameter(
+            "curve_name",
+            label="Temperature calibration curve name",
+            parameter_class=GroupParameter,
+        )
+        """
+        Temperature calibration curve name
+        for the current curve as selected by ``curve_number``
+        """
+        self.curve_sn: GroupParameter = self.add_parameter(
+            "curve_sn",
+            label="Temperature calibration curve SN",
+            parameter_class=GroupParameter,
+        )
+        """
+        Temperature calibration curve SN
+        for the current curve as selected by ``curve_number``
+        """
+        self.curve_format: GroupParameter = self.add_parameter(
+            "curve_format",
+            label="Temperature calibration curve format",
+            get_parser=int,
+            val_mapping={"mV/K": 1, "V/K": 2, "Ohms/K": 3, "log Ohms/K": 4},
+            parameter_class=GroupParameter,
+        )
+        """
+        Temperature calibration curve format
+        for the current curve as selected by ``curve_number``
+        """
+        self.curve_limit: GroupParameter = self.add_parameter(
+            "curve_limit",
+            get_parser=float,
+            label="Temperature calibration curve limit value",
+            parameter_class=GroupParameter,
+        )
+        """
+        Temperature calibration curve limit value
+        for the current curve as selected by ``curve_number``
+        """
+        self.curve_coefficient: GroupParameter = self.add_parameter(
+            "curve_coefficient",
+            get_parser=int,
+            label="Temperature calibration curve coefficient",
+            val_mapping={"negative": 1, "positive": 2},
+            parameter_class=GroupParameter,
+        )
+        """
+        Temperature calibration curve coefficient
+        for the current curve as selected by ``curve_number``
+        """
+        self.curve_parameters_group = Group(
+            [
+                self.curve_name,
+                self.curve_sn,
+                self.curve_format,
+                self.curve_limit,
+                self.curve_coefficient,
+            ],
+            get_cmd=lambda: f"CRVHDR? {self.curve_number()}",
+        )
+
 
 class LakeshoreModel336(LakeshoreBase):
     """
diff --git a/src/qcodes/parameters/group_parameter.py b/src/qcodes/parameters/group_parameter.py
index be8100c3edb..89b5e58482f 100644
--- a/src/qcodes/parameters/group_parameter.py
+++ b/src/qcodes/parameters/group_parameter.py
@@ -149,7 +149,10 @@ def __init__(self, name, address, **kwargs):
         set_cmd: Format string of the command that is used for setting the
             values of the parameters; for example, ``CMD {a}, {b}``.
         get_cmd: String of the command that is used for getting the values
-            of the parameters; for example, ``CMD?``.
+            of the parameters; for example, ``CMD?``. Can also be a callable
+            that returns a command string, this is useful for the cases where
+            the command string is dynamic; for example,
+            ``lambda: f"CMD {get_id_that_specifies_the_command()} ?"``.
         separator: A separator that is used when parsing the output of the
             ``get_cmd`` in order to obtain the values of the parameters; it
             is ignored in case a custom ``get_parser`` is used.
@@ -168,7 +171,7 @@ def __init__(
         self,
         parameters: Sequence[GroupParameter],
         set_cmd: str | None = None,
-        get_cmd: str | None = None,
+        get_cmd: str | Callable[[], str] | None = None,
         get_parser: Callable[[str], Mapping[str, Any]] | None = None,
         separator: str = ",",
         single_instrument: bool = True,
@@ -309,7 +312,10 @@ def update(self) -> None:
                 f"parameters - {parameter_names} since it "
                 f"has no `get_cmd` defined."
             )
-        ret = self.get_parser(self.instrument.ask(self._get_cmd))
+        get_command = (
+            self._get_cmd if isinstance(self._get_cmd, str) else self._get_cmd()
+        )
+        ret = self.get_parser(self.instrument.ask(get_command))
         for name, p in list(self.parameters.items()):
             p.cache._set_from_raw_value(ret[name])
 
diff --git a/tests/drivers/test_lakeshore.py b/tests/drivers/test_lakeshore.py
index f5415291117..07d4026b17f 100644
--- a/tests/drivers/test_lakeshore.py
+++ b/tests/drivers/test_lakeshore.py
@@ -89,7 +89,7 @@ def ask_raw(self, cmd) -> Any:
             self.visa_log.debug(f"Response: {response}")
             return response
         else:
-            super().ask_raw(cmd)  # type: ignore[misc]
+            return super().ask_raw(cmd)  # type: ignore[misc]
 
 
 def query(name: str) -> Callable[[Callable[P, T]], Callable[P, T]]:
diff --git a/tests/drivers/test_lakeshore_336.py b/tests/drivers/test_lakeshore_336.py
index 5af219e8af6..8ad92cff29f 100644
--- a/tests/drivers/test_lakeshore_336.py
+++ b/tests/drivers/test_lakeshore_336.py
@@ -80,8 +80,8 @@ def __init__(self, *args, **kwargs) -> None:
                 auto_range_enabled=0,  # 'off',
                 range=0,
                 compensation_enabled=0,  # False,
-                units=1,
-            )  # 'kelvin')
+                units=1,  # 'kelvin'
+            )
             for i in self.channel_name_command.keys()
         }
 
@@ -259,6 +259,19 @@ def test_setpoint(lakeshore_336) -> None:
         assert h.setpoint() == setpoint
 
 
+def test_curve_parameters(lakeshore_336) -> None:
+    # The curve numbers are assigned in the simulation pyvisa sim
+    # YAML file for each sensor/channel, and properties of the
+    # curves also include curve number in them to help testing
+    for ch, curve_number in zip(lakeshore_336.channels, (42, 41, 40, 39)):
+        assert ch.curve_number() == curve_number
+        assert ch.curve_name().endswith(str(curve_number))
+        assert ch.curve_sn().endswith(str(curve_number))
+        assert ch.curve_format() == "V/K"
+        assert str(int(ch.curve_limit())).endswith(str(curve_number))
+        assert ch.curve_coefficient() == "negative"
+
+
 def test_select_range_limits(lakeshore_336) -> None:
     h = lakeshore_336.output_1
     ranges = [1, 2, 3]
diff --git a/tests/parameter/test_group_parameter.py b/tests/parameter/test_group_parameter.py
index 53929efd5ab..974ec8b4478 100644
--- a/tests/parameter/test_group_parameter.py
+++ b/tests/parameter/test_group_parameter.py
@@ -1,12 +1,15 @@
 import re
 from datetime import datetime
-from typing import Any
+from typing import TYPE_CHECKING, Any
 
 import pytest
 
 from qcodes.instrument import Instrument
 from qcodes.parameters import Group, GroupParameter
 
+if TYPE_CHECKING:
+    from collections.abc import Callable
+
 
 @pytest.fixture(autouse=True)
 def close_all_instruments():
@@ -23,7 +26,7 @@ def __init__(
         initial_a: int | None = None,
         initial_b: int | None = None,
         scale_a: float | None = None,
-        get_cmd: str | None = "CMD?",
+        get_cmd: "str | Callable[[], str] | None" = "CMD?",
     ) -> None:
         super().__init__(name)
 
@@ -60,7 +63,9 @@ def write(self, cmd: str) -> None:
         self._a, self._b = (int(i) for i in result.groups())
 
     def ask(self, cmd: str) -> str:
-        assert cmd == self._get_cmd
+        assert self._get_cmd is not None
+        get_cmd = self._get_cmd if isinstance(self._get_cmd, str) else self._get_cmd()
+        assert cmd == get_cmd
         return ",".join(str(i) for i in [self._a, self._b])
 
 
@@ -85,6 +90,23 @@ def test_sanity() -> None:
     assert dummy.b() == 10
 
 
+def test_get_cmd_being_a_callable_that_returns_a_string_works() -> None:
+    dummy = Dummy("dummy", get_cmd=lambda: "CMD?")
+
+    assert dummy.a() == 0
+    assert dummy.b() == 0
+
+    dummy.a(3)
+    dummy.b(6)
+
+    assert dummy.a() == 3
+    assert dummy.b() == 6
+
+    dummy.b(10)
+    assert dummy.a() == 3
+    assert dummy.b() == 10
+
+
 def test_raise_on_get_set_cmd() -> None:
     for arg in ["set_cmd", "get_cmd"]:
         kwarg = {arg: ""}