An exhaust gas temperature sensor diagnostic system includes an exhaust gas temperature sensor, a controller and a storage device. The controller is programmed to wakeup after a predetermined time after engine shutdown, determine a temperature of the sensor and ambient temperature, calculate a difference in the temperature of the sensor after wakeup to a temperature of the sensor at engine shutdown, determine an estimated temperature of the sensor based on the ambient temperature and the predetermined time, add the difference in the temperature of the sensor at wakeup to the estimated temperature to determine a compensated estimated sensor reading, determine a difference between the compensated estimated sensor reading and a corrected sensor reading, compare the difference between the compensated estimated sensor reading and a corrected sensor reading to a threshold to determine whether the sensor is operating properly. The storage device is configured to store information related to the sensor.