A thermostat diagnostic apparatus is provided with a cooling medium temperature sensor, an engine operating condition sensor and a malfunction diagnosing device. The malfunction diagnosing device is configured to diagnose a stuck-open malfunction of a thermostat provided in a coolant flow passage of an engine installed in a mobile body based on a comparison of a real cooling medium temperature detected by the cooling medium temperature sensor and an estimated cooling medium temperature estimated based on an engine operating condition of the engine detected by the engine operating condition sensor. The malfunction diagnosing device determines that the thermostat is stuck in an open state upon determining that either the estimated cooling medium temperature or the real cooling medium temperature exceeds a prescribed reference value during a period in which an increased heat exchange rate condition of a radiator is satisfied continuously.