I have exactly the same problem with mine, purchased 1983. The red hot spot developed at the junction of a tiny hairline crack in the form of a T, so essentially at a tiny hole. If you put your food directly covering this crack, you can continue to use the oven. The crack will continue to grow, and eventually the base will break while you're cleaning it. Be careful, the edges will be very sharp! The base of mine broke apart last week, after about nine months since I noticed the problem. I would replace the base, if I knew where to buy a replacement base. It's too risky trying to guess what the material is. I always thought it was white plastic, and possibly the surface has a layer of white plastic, but from its weight I'd say it's more some kind of white glass or ceramic.
Lilian Cortis, June 2007