The vintage/age of the hotplate in question is important in
determining
what type of insulation you are dealing with...

Bought it about 3 years old.

BTW, I found the defect. Apparently one of those loose fiber got between the
(mechanical) thermostat contacts. The solution is simple: I pull a piece of
paper between the contacts and now it conducts.

I'm inclined to not put the fibrous insulation back in this thing to avoid
more loose fibers. However, I need a 1-inch thick, heat resistant and
slightly elastic material to push the heating sheet tight against the top
surface.

I think several folded oven mittens may work but is there a better
alternative?