I went to a best buy last year, there was a PS3 they had out (phat model) strapped with security devices all over and it was sitting upside down (On top of the air intake) and they leave it running like that all day, the exhaust air was hot as hell (my phat PS3's exhaust is never this hot). Looks like it's been there for years. If that's not reliable, I don't know what is. :p
You can keep your saves ... just pull the Hard drive out, that doesn't effect the warranty at all. You can back them up on a PC if you like. The PS3 uses 2.5" (laptop style) SATA HDDs.
The model I'm fixing now (with the blown caps) is also a launch 60GB model.
All Xbox 360 slim did was cut two more holes in the sides and add a massive fan to DIRECTLY cool the CPU and GPU. Which the other 360 model did not have (the DVD drive sat on top of those heat syncs ... stupid design)
And, I don't know if I'd trust Sony to send back another BC PS3 to be honest. Unless you can get a written guarantee from them, I wouldn't risk that. Those things, even broken, can go for over $150. Refurbished ones are like $300. They are VERY sought after.
Also, what happens when you turn it on? Like, exactly. It might be easier to give a recommendation if we have an idea why it's giving YLOD.