I used a variation on the "hairdryer fix", but instead of putting it into a closed space and heating it blindly like the sheep that most people are. I stripped all the components apart (card reader, power supply, bluray drive, on/off/eject plate, back plate and the battery that connects to the motherboard).
Then I put only the PCB (the metal plate which 'sandwiches' the motherboard) as well with the fan, back into the lower case (so it would keep the entire structure levelled).
Then I used the hairdryer on it for 15 minutes. The first time I did it, I was blowing it directly at the under-side of the GPU (since when you keep the PS3 horizontally, the processors are actually flipped facing down). It didn't work.
So then I did the same thing, but got myself a 2nd fan, and removed the plate which squeezes the fan to the GPU (I didn't even look at the CPU, since it doesn't cause any problems). 1 Hairdryer was blowing on the reverse side of the motherboard (under the GPU) and another one into the vent from the back which goes directly to the GPU. After 5 minutes I carefully put the plate on and screwed it in and then proceeded to continue blowing hot air on it.
During this process you can hear cracks coming from either the motherboard (which when the 1st time I opened it, it was visibly twisted). After the 15 minute mark I lowered 'gears' on the hairdryers until it got to cool wind, so it would rapidly cool the motherboard as well as the hairdryers themselves.
Then I slowly moved the PS3 under some cold AC wind to allow everything to rapidly cool and hopefully remain soldered in the right places.
After about an hour I reassembled the whole thing. And surprise IT WORKS!!!
I knew the hairdryer would work, since it basically is supposed to do the same job as a heatgun, but much slower and less efficient. But simply heating it without removing all other components is moronic, to say the least.
The cables and connections can melt, non-dissipating heat will just shorten the life of the various components and that small battery on the motherboard could end up exploding. Also not to mention that the plastic WILL melt, especially the one covering the fan exhaust.
The physics behind this is: you're recreating a gaming session which led you to this situation in the first place. Because the processors will run at about the same temperature as your hairdryer will reach.
The first thing you want to do, if you get your fixed PS3 running is sync your trophies, back up the save games (which are possible) of the games you're currently playing. And then deactivate all PSN accounts on that console, because you can only share up to 5 accounts.
If it's still running, then shut it down. Wait for your new PS3, and then using an ethernet cable (SOLD SEPARATELY
for most) transfer all your stuff to the newer model then drive up to your closest Sony center and beat the living crap out of all the workers there for working for a company which built it's high-end product to surely break.
Now I've written a huge post on this (the above is just the sample concerning OP's main request) but because I used explicit language, I think it's best to simply link to the source, if anyone does want to read my full story :-(
http://www.eojmarket.com/index.php?topic=1957.msg13253
Good luck OP!