Yes, they do get warm / hot. They work by reducing the voltage to the motor by resistance. Some like the Singers use a carbon pile, others use wire resisters. Either way the slower you go the more the voltage is reduced. This voltage has to go somewhere so it's dissipated as heat. Some controllers get hotter than others.
I have some I can't sew slow on without a shoe. Others are fine. I think it's age and use that contributes to them getting hot.
I also use one of those silicone iron pads under the controller on a carpeted floor.
As for damaging the machine, don't worry about that, the controller is doing what it's supposed to.
Joe