Very useful advice thanks.
It is a 1.1 machine
The first time it shut down I'd just got it home and was trying it out so put it on the (short-pile) carpet after carefully checking there were no vents on the actual bottom. 15 mins later of playing GTA it had had enough!
The second time was at the end of using dvd2xbox to copy Halo over to my hard drive which makes you think it was the drives generating heat. The drive I've fitted is a 7200rpm model but it's a new Western Digital one so didn't think it would get too hot.
Am tempted to try that fan though but will keep an eye on it first and try and work out if there's a pattern to it.