If I may set a timer on Friday to turn lights on/off on Shabbat, may I also set a timer to start an electric urn so that the urn will begin to boil water on Shabbat morning? (The water in the urn was not previously boiled.) My sense is that the answer should be "no", but I’d like to know what the difference is between timers that turn on lights and timers that turn on cooking appliances.

Indeed the answer is no, and the problem is because of the prohibitions involved in use of fire and heat to warm food on Shabbos. If you can read rabbinic Hebrew, I can send you a copy of my teshuva on the subject of use of coffee makers on a Shabbos clock.