RROD Error 0013 - Ram Overheating. The fans spin up to Mach one and then the machine shuts itself down to prevent further damage.
I reflowed the solder in addition to installing the RROD Fix Kit from iFixit. The machine has been working great since I put it back together, but only time will tell if it holds.
If you're patient, you can clean the thermal paste off the processors with rubbing alcohol alone. I bet Goof Off helps immensely, but in a pinch alcohol will do. I used Q-tips liberally for that part.
Also consider having someone help hold the motherboard up while you are applying the washers and screws for the heat sinks. Trying to do that with only two hands may raise your blood pressure significantly.
Also some canned air might be wise for cleaning out the blades of the heat sinks.