I've had the same problem with the foot controller on the 2005 White sewing machine I inherited from my mom. My old Featherweight foot controller works great - never a heat problem with the old one and the replacement new one I got a couple of years ago when the plug in broke on the machine. The White foot controller gets so hot it starts to scorch the non-slip pad I was using to keep it from moving over the carpet.
I finally gave up and just have to remind myself to shut off the machine every so often to let it cool down. It only seem to happen after about an hour or two of sewing, so I usually need to take a break from sewing anyway.
I think it's a design flaw with the newer foot controls. I think the manufacturers just are trying to keep costs under control and they don't care if their customers have problems with overheating....this way they can sell a new machine.