The card also gets power from the PCIe slot as well.
If you have a DMM (digital multimeter) and you know how to use it you can use the paperclip test to test the voltages from the PSU to make sure that they're all OK.
If they are OK then the GPU card will have to be checked and tested.
Heating up the card means disassembling the GPU card and baking the circuit board in an oven to try and “reflow” the circuit board so that any faulty solder connections are resoldered by the heat. In my view this is not a good thing to do as it can cause more damage, but I’m old school. The trick with this is knowing the correct temperature and for how long. Too cool will do nothing, too hot will damage the circuit board.
Without a schematic of the GPU card, (I couldn’t find one online) it would be very difficult to find out what the actual problem is unless there was an obvious component fault e.g. burnt out, but then you would have to know what is it (may be unrecognizable) and also work out why it happened.