3. It does seem like an external serial modem is the next best option, although then I have to provide power to both the Arduino and the modem. The power in the building is not entirely reliable. I could run the Arduino off of the telephone line, I think, but I'm not sure how to do that for the modem, which uses conventional 120 volts. I suppose I could take the modem apart and try to supply whatever it needs internally.
4. In order not to need a dedicated computer elsewhere that the Arduino is calling, I think it might be better to have the Arduino accumulate temperature data in its own memory and then I will call it when I want to know what's going on. I'll have to figure out how much memory is available for data storage. And this would require the modem to be on all the time so that it could listen for my call.