diff --git a/custom_components/sat/heating_curve.py b/custom_components/sat/heating_curve.py
index ec9ca74b..4a927923 100644
--- a/custom_components/sat/heating_curve.py
+++ b/custom_components/sat/heating_curve.py
@@ -28,9 +28,12 @@ def update(self, target_temperature: float, outside_temperature: float) -> None:
         heating_curve_value = self.calculate(target_temperature, outside_temperature)
         self._last_heating_curve_value = round(self.base_offset + ((self._coefficient / 4) * heating_curve_value), 1)
 
-    def calculate_coefficient(self, setpoint: float, target_temperature: float, outside_temperature: float) -> float:
-        """Convert a setpoint to a coefficient value"""
+    def calculate_coefficient(self, setpoint: float, target_temperature: float, outside_temperature: float) -> float | None:
+        """Convert a setpoint to a coefficient, if the curve is nonzero."""
         heating_curve_value = self.calculate(target_temperature, outside_temperature)
+        if heating_curve_value == 0:
+            return None
+
         return round(4 * (setpoint - self.base_offset) / heating_curve_value, 1)
 
     def autotune(self, setpoint: float, target_temperature: float, outside_temperature: float):
@@ -39,6 +42,9 @@ def autotune(self, setpoint: float, target_temperature: float, outside_temperatu
             return
 
         coefficient = self.calculate_coefficient(setpoint, target_temperature, outside_temperature)
+        if coefficient is None:
+            return
+
         self._coefficient_derivative = round(coefficient - self._optimal_coefficient, 1) if self._optimal_coefficient else coefficient
 
         # Fuzzy logic for when the derivative is positive
diff --git a/tests/test_heating_curve.py b/tests/test_heating_curve.py
new file mode 100644
index 00000000..624ad9fd
--- /dev/null
+++ b/tests/test_heating_curve.py
@@ -0,0 +1,37 @@
+"""Autotuning cannot infer a coefficient from a zero-valued curve."""
+import pytest
+
+from custom_components.sat.const import HEATING_SYSTEM_UNDERFLOOR, HEATING_SYSTEM_RADIATORS
+from custom_components.sat.heating_curve import HeatingCurve
+
+
+@pytest.mark.parametrize("heating_system", [HEATING_SYSTEM_UNDERFLOOR, HEATING_SYSTEM_RADIATORS])
+@pytest.mark.parametrize("restored", [False, True])
+def test_zero_curve_autotune_preserves_history(heating_system, restored):
+    curve = HeatingCurve(heating_system, 2.0)
+    control = HeatingCurve(heating_system, 2.0)
+    if restored:
+        curve.restore_autotune(2.0, 0.4)
+        control.restore_autotune(2.0, 0.4)
+    before = (curve.optimal_coefficient, curve.coefficient_derivative)
+
+    assert curve.calculate(20, 20) == 0
+    curve.autotune(35, 20, 20)
+    assert (curve.optimal_coefficient, curve.coefficient_derivative) == before
+
+    curve.autotune(35, 21, 10)
+    control.autotune(35, 21, 10)
+    assert curve.optimal_coefficient == control.optimal_coefficient
+    assert curve.coefficient_derivative == control.coefficient_derivative
+
+
+@pytest.mark.parametrize("heating_system", [HEATING_SYSTEM_UNDERFLOOR, HEATING_SYSTEM_RADIATORS])
+def test_coefficient_is_undefined_for_zero_curve(heating_system):
+    curve = HeatingCurve(heating_system, 2.0)
+    assert curve.calculate_coefficient(35, 20, 20) is None
+
+
+@pytest.mark.parametrize("heating_system, expected", [(HEATING_SYSTEM_UNDERFLOOR, 5.5), (HEATING_SYSTEM_RADIATORS, 2.8)])
+def test_nonzero_curve_coefficient_is_unchanged(heating_system, expected):
+    curve = HeatingCurve(heating_system, 2.0)
+    assert curve.calculate_coefficient(35, 21, 10) == expected