Xbox 360 Reflow
In December 2012, a used Xbox 360 was purchased. The machine in question had a manufacture date of 2006, so it was assumed that the RROD was inevitable. Sure enough, after about two months, it failed.
There are hundreds of guides out there for taking apart an xbox 360, so I won't go into detail here. You need a T10 and T8 screwdriver, and something to pop out the plastic clips holding the case together.
When you remove the heatsinks, you will need to thoroughly clean up all the old thermal paste from the chip dies and the heatsinks themselves. Alcohol, methanol, or acetone work great for this. Use a plastic spludger to remove all the paste from around the edges of the chips.
Using a dual heat hot air gun/paint stripper, heat the bottom of the board (under the two main chips) for about a minute on low heat with the gun about a foot away from the board. Carefully flip the board over, move the gun to high heat, and heat the tops of the chips for about 4 minutes. Let the board sit at least 30 minutes to completely cool with absolutely no disturbances.
Don't use anything but a high grade paste like arctic silver. Apply a small amount of paste to a plastic bag or piece of syran wrap pulled over your finger, and rub the chip dies to apply a very thin layer. Remember - thermal paste is only there to fill the small gaps between the chip and heatsink, NOT to act as a thermal conductor between the two. Too much paste will insulate the chips and cause them to fail all over again.
Do not apply any paste to the heatsinks.
Most xboxes use “x-clips” to retain the heatsinks, but mine came with screws and nylon washers for some reason. It's doubtful yours will, so you will need to find the appropriate screws and nylon washers. There are lots of guides suggesting a variety of different types of screws - I have no idea what works best or what I have, so you will have to look around.
I chose to leave the plastic case off mine - plastic is a wonderful insulator which means it's terrible for an overheating xbox. I also used a dremel to cut away the metal grill on the outside of the fan. Removing the grill provides greater air flow and better cooling.