@wnlewis the issue here is not the cooling of the chip but the design of it. The processor is a flip chip design and the issue for the failure is commonly caused by the solder bumps between the IC and the substrate. The proper definition of that can be found at Wikipedia "is a method for interconnecting semiconductor devices, such as IC chips and microelectromechanical systems (MEMS), to external circuitry with solder bumps that have been deposited onto the chip pads." It does not matter if it is a MBP a PS3 or a XBox, due to the constant heating and cooling of the IC, the bumps that connect the chip to the substrate lose contact and your chip (in this case processor) fails.
As you can see the "bumps" are what actually connects the die to the substrate to make the chip complete. If these bumps fail, the die does no longer make contact with the substrate and thus no contact with the circuit board. The chip has failed.
Here you can see the space where the bump has failed and no longer makes contact. We are talking microns of space here.
Sometimes a bit of pressure on the top of the die potentially close the gap. Same with a reflow, which may allow some of material from the bump to reshape and starting to make contact again. The heating of cooling of the chip during use is what will eventually cause it to fail again.
If you are going to do a reflow then the general guidelines for a good profile would be something like this:
Temperature ramp up 1ºC/second
Peak temperature should be 200C to 210C
Remain above liquidus (183C) for 45-75 seconds
Do not heat any packages above 220C since this will most likely destroy the IC. Sure, you could just blast the chip with some hot air and it may or may not work, but it'll be a bit of a crap shoot. Through the whole Xbox and PS3 debacle of those failed chips, I invested in a IR reflow station. It was something like $250 USD on ebay and used that for a few successful repairs.
Here is a good document that will help you with the profile as well BGA-Reflow-Rework.pdf.
Now, to replace the chip completely, you are looking at a reball. Which is far more involved and will require some practice and definitely the right rework station. For that you need the right stencil, the right balls as well as a reballing station (those are not to expensive).
Everything on here can be learned by practice but the main challenge will be to find a replacement. You will most likely only find used ones (maybe from a functioning board) but because of the actual design, you just will not know how long it is going to last. You'll be spending a lot of money on something that may only be temporary. So, blasting it with a hot air gun may just be a more economical attempt to revive this. At least get a thermometer and some thermocouples so that you get within the ballpark of the right temperature.
As for the liquid inside the heatpipe, we don't know what Apple uses but for computer cooling applications the common combination has been copper as a fluid container and water as a working fluid. Other working fluids can be ethanol, acetone, and even ammonia. Flammability is an issue and that is why fluids like ethanol etc. are not commonly used. Since these heat tubes are either filled under vacuum, the DIY'er can't really repair those.
As you can see, it will all depend on how far you want to go with all of this and how much money you are willing to invest. Anything is possible, just a matter of how many resources you want to mobilize.
This is just a quick and dirty explanation of what has commonly affected the flip chip designed GPU.
Repair is War on Entropy!