If you see a significant difference between the two values, it would be a good idea to check the aircraft TAT vs. what the tower is reporting. Aircraft TAT sensors are usually heated but also aspirated so that they give accurate readings without forward airspeed. However, that aspiration can fail or the TAT sensor get obstructed with bugs or other debris which can adversely affect the TAT reading. Although commercial aircraft have 'dual' TAT sensors, they are usually in the same probe so they are not truly independent measurements (off hand, the 747 is the only Boeing aircraft I can think of that has dual TAT probes as basic).