Just a little update, and a link to some software that's useful (and free).
With the computer on it's side, and the other side panel removed,
and an extra fan stood inside the case to stir the air around a bit, I left it running overnight.
I also installed CPUID Hardware Monitor
http://www.cpuid.com/softwares/hwmonitor.html which I left running.
This is a great little free program that will display various sensors that your motherboard makes available, and with this I was able to see the CPU temperature, hard disk temperature etc.
It also tracks minimum and maximum values for each sensor, as well as current readings.
So, overnight, the CPU was running at 40C, with a peak at 41C. Not bad. And it didn't crash!
Just now, I tried putting the side of the case back on, but leaving the additional fan inside, and leaving the computer sitting on it's side. Within 15 minutes the CPU temperature had crept up to 50C, at which point I removed the lid again, and it slowly dropped once more to 40C.
I'm assuming then that there are two problems, as I can't see why it crashes so quickly when it's upright if its a temperature problem alone. It takes less than a minute to boot from cold, yet you can't log in when it's upright - it blue screens on you as it's loading the desktop!
Just thought I'd share this in case it's of interest really!
Ian