This issue is most certainly caused by poor cooling design in the HP DV series notebooks.
The problem is caused by a few of things.
1. The Sticky thermal pad used to transfer heat from the Nvidia GPU to the heatsink which does not do its job
2. The fan speed and internal design do not allow enough hot air to be extracted from the casing.
3. The use of lead-free solder which is more brittle and easily cracks under high heat conditions.
There are a few ways to fix it.
The blanket method works because it overheats the GPU (and the whole board which is not really a good idea) and in turn re-balls the solder joints under the GPU this method is not recommended.
The heat gun method does the same thing but the main danger is overheating nearby components. Done correctly this works and has so far been effective as long as you insulate the heat using tin foil (aluminum foil)
The professional way to correct this problem is typically done by using hot air or infrared re-balling techniques where you remove the GPU, clean the old solder from it and re-ball the small GPU points and re-attach to the main board.
I would also advise replacing the gooey thermal pad stuck to the GPU with a 2mm thick Copper sheet cut to about 7mm by 8mm made from 2mm copper sheet.
Use arctic silver on the both GPU core and on the top of the copper heat sink.
This should keep the GPU about 10 degrees Celsius cooler compared to the stock HP DV2000.
If you use a notebook cooler pad with the notebook this should be enough to keep the machine working for awhile.
Hope this helps.
Drop me a line if you need assistance.