Like many others before me, my 80gb Metal Gear Solid PS3 early edition Fat console also got the YLOD this past weekend. (July 2013) After many hours of research I came across many of the answers listed on this page. I wanted a more permanent solution rather than a temporary fix and here is what I found out.
Obviously, if it is still under warranty, call Sony and they will repair it for free. No brainer. Only problem is you will lose all your saved game data as you will not be getting your old system back. But free is free.
If you try the heat gun solution, it will likely work, but like most will tell you, it won't last forever, especially if you play the system a lot. You need to baby it from here on out. Only playing for 1 or 2 hours and then shutting it down and letting it cool. You will need to ensure proper ventilation, probably put a fan back there to aid in the air flow. Make sure the PS3 is away from the wall, off the carpet, etc... The good thing here is if it works you can get your stuck disc out, and maybe backup your saved game data, and who know maybe get a few more months of it, but it will happen again.
Another option is to send it off to get repaired by a 3rd party such as Gophermods.com. Although I didn't use them, there are a lot of happy customers, and they deal specifically with the YLOD. Their website lists a YLOD fix for $79.99 and it includes free shipping and a 24hr turn around time once they get the unit. You get your stuck disc back and you keep your saved game data. They will also give you a 6 month warranty as long as you follow the recommended playing time after the fix. (2 hrs on, 30 min off - For like the 1st 200 hours of game play.) That service is for a reflow of the solder, and they have all the proper equipment and use an upgraded solder, but they will tell you it is not a permanent fix. They also do a reballing service, although I didn't see it listed on their website. I think it is like $130 or $140, but from what I understand it is a better fix but they have a wait list to get that done. I think you need to call them and ask for more details on the service to get a better idea of if it makes sense for your situation.
I also looked at just buying a new system from the store. But with PS4 systems coming out in less than a year I didn't really want to waste the $$. A new 250gb PS3 was $250. I really only need my PS3 to make it another year, as I anticipate buying a PS4 6-8 months after launch. Hopefully all the major bugs will be worked out by then. You can also save some cash by looking at buying a used system from Gamestop or on eBay. I personally don't like that option as there is no telling if your buying a system that has also had the YLOD but someone fixed it using the blow dryer. Buyer beware.
Finally I just called Sony Customer Service (# found in the PS3 manual) and talked with a representative. She stated that I could trade in my PS3 80gb fat player for a new or refurbished 250gb PS3 for $129. (There may be different deals for different systems, i.e. 40gb, 60gb) I was past my warranty, but Sony is obviously trying to right a wrong with the YLOD problem. It kind of sucks paying $600 for my initial unit and not even having it last 5 years and then pay another $129 on top of that, but like I said, I was out of my warranty, and Sony didn't really have to do anything. She said the only drawback was that I would lose all my saved game data unless I had backed it up on the 'cloud' system and that the new systems were not backward compatible with PS1 and PS2 games. She said that they would return my game that was stuck in the player, and they would pay for the shipping by sending me a shipping box with a UPS label already on it.
It all depends on what is important to you, but for me, getting a reliable PS3 system going forward was more important the the saved game data I was losing. I was getting my game back, and I didn't have to worry about the solder problem coming back to get me in the next 2-3 months. I asked the Sony rep if I could try the heat gun fix to get my game out and possibly back up my system, but she said if I caused more damage to the system, then Sony could void the agreement that we just made and would not give me a new system. If you've already done it, I wouldn't bring it up, but I'm sure they are checking the systems when they come in.
Getting the YLOD is devastating, but with a little patience and a cool head, you can find a number of solutions that are available. It's unfortunate that so many had to experience this problem, but all the on-line comments helped me figure out what to do. I just wanted to put it all in one post to hopefully help out the next person.