I've repaired a couple of Mac's by removing the videocard, stripping it from all thermal-fluid, plastic etc. Put in in the oven for 8-10 minutes at 200 degrees Celsius , and putting it back (using new thermal pasta). This will let the soldier melt a little bit so any short-circuits don't appear anymore causing the GPU to work again.
it's difficult and time-consuming but it beats replacing a GPU for a lot of $ (or € in my case :)
And some PC laptops have the exact same problems with the GPU. Sometimes the thermal pasta or copper heatsink won't be doing it's job right causing the GPU to get real hot and fail eventually. A lose connection with one of the chips is mostly the case (also from using environmental friendly soldier)..