OK OK. Luckily the thread started on a cooling problem. Heat is a much harder issue to provide backup for and some systems can be deadly!
No, not at all. It's much easier to provide back-up for heating than cooling. Many gas g.h. heaters are run by the pilot light(always on and burning a little gas) and get triggered on and off by the theromstat. No electricity needed. Littlefrog is right though, some have more systems interconnected that do use electricity, like powered venting and forced air in large g.h's. Most homes have forced heating so need the electricity.
My southern burner has a small fan in it as well but it's also gas driven, not electricity. It comes on automatically when the gas is ignited. You don't need any sort of generator or outside power source if you get a thermostat that's run by battery. The battery would give it the power to "tell" the gas heater to turn on or off. I got mine at Home Depot or Lowes and it wasn't that expensive. The batteries last about a year and you get a low battery warning on the thermostat so it won't go out on you. It frees up and electic outlet and gives you the luxury of not worrying about power outage.
Think of it this way...many gas heaters are not electricity dependent and don't need electricity to run, only to "tell" them to go on or off and a battery powered device can do this. It really depends on what type of heater you have.
One heater back-up problem is that if the pilot light gets blown out somehow during the winter and there's no temperature alarm, you're screwed.