Low range limiting malfunctions of an engine coolant temperature (ECT) sensor are diagnosed by comparing a change in the sensed temperature during engine operation with a calibrated temperature change. If the change in sensed temperature fails to exceed the calibrated temperature change, and a diagnostic for detecting a stuck ECT signal is either inconclusive or passed, a low range limiting malfunction of the sensor is indicated. If the diagnostic for detecting a stuck ECT signal is failed, the low range limiting diagnostic concludes with no report even if the change in sensed temperature fails to exceed the calibrated temperature change.