How does fan relay work?

A common fan delay relay works by a small thermal coil contained within it. Upon application of the low-voltage control signal, usually 24 v, the coil begins to heat up and after a pre-determined amount of time, will cause the primary contacts to close. This allows the furnace to fire up and warm the heat exchanger prior to the circulation fan coming on. At the end of the heating cycle, the control voltage is removed and again, after a period of time, the thermal coil will cool down, opening the primary contacts and shutting off the circulation fan. This ensures an adequate flow of air over the heat exchanger after the burner is extinguished, purging the system of any remaining heated air. Even though it may contain a thermal circuit, it essentially is still a mechanical relay and thus subject contact stick, mechanical damage, etc. Many of them have been replaced with a solid-state relay and control/ delay circuitry.