An onboard cooling system diagnostic strategy utilizes at least one temperature sensor fluidly positioned between an electronically controlled engine and a thermostat. The diagnostic algorithm operates by monitoring coolant temperature during engine startup. By comparing the actual coolant temperature during engine start-up to a predicted coolant temperature that should occur if no cooling system error is present, a cooling system fault condition may be identified. If a cooling system fault is detected, the diagnostic logic may activate the engine cooling fan or intrusively open an electrically controlled thermostat while monitoring the coolant temperature response to the intrusive action. If there is a substantial change in coolant temperature responsive to the intrusive action, this phenomenon can be utilized to correctly distinguish between a thermostat failure and a vehicle configuration error corresponding to an overcooled vehicle. The present disclosure also can utilize a similar strategy to diagnose problems associated with other vehicle fluid coolers that exchange heat with ambient air moved by a circulation fan.