The machine has been in the store over the weekend, and they replicated the overheating problem. Apparently it got referred to the head of their repair people, and after 5 days they called me to say that they would replace it, by store vouchers which would be sent through to the store to save time. Total value of the vouchers £529, cost of purchase of the machine £649.
I wasn't overly impressed with the offer, but they said that there was a machine of similar specification in the store retailing at £529, and they would replace like for like. I asked what would happen if I wanted a cash refund, and they said that it would be for a maximum of £529. Said I would have to think about this.
Not too sure of the Sale of Goods Act here, but seems to me that if I'm sold an item for £649 and it is deffective, then if I return it and want my money back, I want all my money back. Also, if it is deffective I do not have to accept a replacement, and in a fast moving arena like computer hardware a like-for-like replacement is frankly insulting when you haven't had use of the machine for 6 months.
In the midst of contemplating this, I got another call about 2 minutes later. I now have vouchers for £529 from the extended warrenty side of the business (though I didn't take an extended warrenty, the machine is still under the 12 month guarentee), and the store will make up the £120 difference between that and the receipted cost of my original machine. OK, so I have to get my new machine from PC World, and run the risk of crummy service should that one be defective too, but (eventually) I've got pretty much what I want. Also seems that PC World are pretty keen not to let any money out of the business once they have it, but that in turn can be used to your advantage.