I know it's rather cheeky of me to ask for help without contributing much towards the community
not at all -- we don't view things that way here -- everyone is welcome to ask for help when they need it.
you're already way ahead of most people in diagnosing your problem.. and it's highly likely you have correctly identified why your computer is spontaneously shutting down. not only that but figured out a fix for it.
i'm not a hardware expert by any means, but it kind of seems unlikely to me that the heat is responsible for the wireless card losing it's connection.. just because there seem more likely culprits, like the normal annoying dropped connection that occurs relatively frequently for everyone. wireless usb adapters and pcmcia cards are very cheap these days, and it may pay to just buy one and see if it solves your issue.
[i had a problem with my old laptop suddenly being unable to go to standby properly after i upgraded to windows xp sp3.. after a day of struggling i just said sod it and bought a new $20 network adapter card and the problem was solved; sometimes it really is easier to just replace something than figure out what particular gremlin is on your wing. however -- if you have a built in network adapter in your laptop that may not be a viable option, though it would be useful if only to tell you if overheating is the the cause].
As for your My Computer issue, i don't know.