And a fried computer because video cards aren't hotswapable.
You can't shut it off, but you can underclock the hell out of it. Rivatuner or coolbits should allow you to downclock the core and memory. Fire up bittorrent, then load coolbits and take the clocks down to 300/300 (for example). Turn off your monitor and go to work. It will still emit some heat, and consume some energy, but they will both be lower amounts then before.
Last, if you're having some temp problems, consider buying a few fans.