I have a Bryant Heater on upstairs ofmy central unit. I can light my pilot light and the unit will start heating. The it shuts off. The fan continues to blow and the heater still works, but the pilot light goes out and has to be re-lit. Is that the thermocouple? I have a Bryant 394had036050 series B. Serial # 3293a15950

Is that the thermocouple?, ((yes )),probably,they are cheap and easy to replace

While you have it apart you might also clean the pilot orifice to be sure you get a good pilot flame.