G35-av650 GPU solder problem

As far as the solder question, it's done with something that looks like a big meat tenderizer (picture a whole bunch of soldering iron tips heated all at the same time). Very intense to do with something of your own. You'd have to find a soldering iron with a very small tip. You might try finding a heat sink that's the size of the chip and saw off the fins until it fits between the motherboard and chassis (or wherever). For fun I took apart an old laptop. They used a fan similar to one that connects to the card slots in the back of a desktop PC. The fan exhausts along the one edge of the blades. Check out a computer store that sells used equipment and see if they have a PCI/PCIe graphics card that's got a fan for cooling you could use. I know it's going to be hard to find something small enough to fit inside the laptop, but that's a possibility.