I think we all concur that you're having an overheating problem. Now, let's decide what's causing it. Do you hear the fan running at high speed at any point before freeze-up? Obviously, no fan, no cooling when it's needed most, and this seems to be a problem with iBooks that have had the case cracked (opened) by experimenters... something gets unplugged, something gets moved slightly, or the fans simply burn out from being on so much, typically in situations where a person lays the laptop on a blanket, clothing or other area where it cannot vent itself.
If you have high speed fan function, then we can assume your logicboard is sending the signal to cool things off and you'll need to look at applying heat sink paste... after years of heat it does dry out.
Lastly... the advice on a cooling pad under the laptop is always a great idea, but if it will not run properly "without" it then you have to fix that problem first... laptops were designed to run without a cooling pad so if yours will not, the cooling pad will not fix the initial problem. I'd advise that you quit allowing it to overheat to test for timing, etc. and never leave it on for a half hour after it freezes up (it's not going to start back up on its own) - everytime your iBook overheats you're taking a few more months of life out of it. :(