Don't see how changing the 'circuit board' can ever make a difference to a noisy FF.
Noise is most likely to come from a vibrating motor that drives the condenser pump - so changing a circuit board will do nought. It is vaguely possible that noise is coming from the sound of the refrigerent moving through the pipework (it sometimes seems to make a slight squeaky noise).
So you've neen sold a pup.
Regarding your second enquiry I agree that such devices have a thermostat that drives the interval between cooling sessions.



