Is it safe to caulk around a radiator?

I wouldn't worry about it. The radiator won't put out enough heat to cook the silicone unless you put it right on the hottest part of the radiator and it would have to get a couple of hundred degrees at that. Once the silicone is dry, it won't put off any gas. The smell is a result of curing. Even near the stove or oven, I suspect other combustible materials would start to show signs of heat stress before the silicone. But, if you're really paranoid about it, you can go and buy some high temp RTV silicone from the auto parts store. It's used to make gaskets, but I'm not sure it comes in white. I believe GE just started to make a clear silicone that is high temp rated, but it's kind of a liquid, if my memory serves me correctly. As far as the stove or oven, what kind of heat is the area you want to caulk exposed to? Next time you use it, run your hand on it and even if it's hot, as long as you can keep your hand there, you won't have a problem with silicone if it's cured.