i think rickm had a freudian slip and Deborah missed it
switch it off. any insulation you add will increase the peak temperature. if you insulate it perfectly, it WILL self-destruct by melting itself, or reach ignition temperature and burn, whatever occurs first.
you cannot run a heating system without a thermostat, or at least a dimmer.
nothing of what you are doing is safe, and insulating the heat source even better will increase the temps even more and make this dangerous situation even more dangerous. the one safe option is to unplug, and do not plug it in before you have a solution, and test it without the snake inside and verify that its working before you put the snake in.
to keep the snake comfy, for now just increase the room temperature.