The heating guy came back with a replacement thermal switch. He got it put in, and the heater works...and has a cracked heat exchanger. So much for that.
It's a 75000 BTU gas-fired central heater. He's going to come back with a couple of quotes for us. We don't need that much heat. The existing heater is there because a previous owner of the house did auto body work in the garage, and so needed to have it at a comfortable temperature. All we need is to keep it above freezing in the garage. (Actually, that's all I need; Paul doesn't even need that much.) The heating guy is going to quote us a 45000 BTU single heating unit, which should be much less expen$ive. Even so, if it's too much, we'll simply do without.