Comfort Control System problem

1994 Buick century wagon with a 3.1L motor.

The a/c will be running and then just stop, this includes the heater part of the system. But along with this the cooling fans also stop and starts to cause the engine to overheat. But then the A/C will start working again which in turn starts the cooling fans to work too.

My question is does the A/C relay control the whole comfort control system including the heater? I have looked for some main relay for the comfort control system but cannot find any. Also does this A/C relay also control the cooling fans? Is there a way to check the relay as I suspect that it may be failing but not completely yet and that is why is stops working and then starts up again.

Any feedback would be appreciated.

Terry