Well, about the IR port of the axim... it's quite weak, you know... To operate my TV with it I have to be like at least 5 feet near it, and it has a 3 seconds lag. The program I use,
TV remote controller, has a learning function you could use to teach it the IR signals of your Air Condittioning system. The program has a programmable Timer function you could use to tell your AC System when to turn on and off, if you manage, of course, to have the pda near enough...