Fan center controls generally are found in older standard furnaces. These are added to separate the heating side from the air conditioning side and added while air conditioning is installed. Newer furnaces have everything controlled via the control board.
Older atmospheric furnace fans are controlled by temperature and a temperature-controlled fan won’t work for air conditioning since the fan needs to run as soon as air conditioning is triggered on.
The fan center consists of a relay, transformer, and terminal strip for the thermostat wiring ran from the thermostat to the fan center control terminal strip.
The fan center control usually mounts inside the furnace on a 4″ x 4″ junction box.