looked on our trade websites
although not all parts are listed i cant see a circuit board
if it has no board then its likley they use a thermostat mounted at the top to sense the temp and turn on the fan
my approach would be to follow the cables to the fan and see where they go
one will go to common point like an element to pick up a neutral
the other should go to the stat
when you find the stat you need to check it with a meter as when thingd are cool you should not get a reading across it
Dave