Those old foot controllers are resistance units. They use wire or carbon pile resisters to control the voltage. When you sew slowly for an extended amount of time, they get hot. I have several like that. I use silicone iron pads between them and my carpet and like barny said, I sometimes have to stop and take a break. Since I usually sew bare foot I can tell pretty quick when they get hot.
About the only cure is to replace the old controller with an electronic unit. They don't get hot at all. But they are amp sensitive so you have to make sure the controller is rated for the same or higher amp rating as the motor on your machine. Also my only real gripe on the electronic units is they are lightweight plastic and tend to scoot out from under my foot. The factory electronic controllers are better made if you can find one.
Joe