A correctly adjusted button controller/foot pedal, will not get hot when not in use.
Unplug your featherweight from the power source or outlet when you are not sitting there with it!!!
However, a properly adjusted button controller/foot pedal will only get hot when stitching at slow speed for a long time, or at high speed for a very long time.
For safety-sake, UNPLUG YOUR FEATHERWEIGHT when not in use (when not being supervised in person, right there in the room with it, using it).
It should get a good bit warm when slow stitching, that is normal, a part of how they were made to work.
Everything breaks eventually, but do not throw away a button controller because it gets hot when the machine is not stitching. Do see if you can have it adjusted instead. If it isn't broken, a good repair person can adjust it, then leave it plugged in and not running for a half hour or more and check that it stopped heating up.
Aardie.