I've heard those particular cards run hot. While it is not ideal, it won't destroy your card. However, I would suggest possibly looking into an aftermarket cooler if you don't feel comfortable with those temperatures. 80C isn't deadly, but it's getting up there...
Also, check your wiring and make sure nothing is in the way.
Try reseating the cooler with a fresh set of quality thermal paste like Arctic Cooling MX-2. Just did my 4870x2 today, dropped me about 10-15C but I wasn't as high as you to begin with. The reference coolers are more than adequate to cool the card when they are seated correctly and you are running a customized fan profile. Download RivaTuner if you don't already have it and follow the guide here:
I also suggest you underclock the card further than the factory set it to for putzing around in windows, I have mine set to 400core/300mem for Windows although if you set it too low some cards don't like it, I heard alot of people can't lower the core under the factory 500 for 2d mode, it is hit and miss. This can be done with RivaTuner as well or you can just make a custom Ati Overdrive profile and set the core speed leaving the fan to automatic, and let RivaTuner take care of the fan.
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