GPUs do not overheat easily.
I bought an Arctic Silencer 5 for my X800XT a couple of years back, because I thought 80C was a little warm for my GPU and the fan noise of the stock cooler was annoying. A few months later, my graphics card started randomly crashing under heavy, prolonged load. Turned out that the Silencer's fan was stopping whenever the temperature passed 60C, possibly due to bad lubrication in the fan bearings combined with a ****ty motor. The GPU would hit 120C before it started acting weirdly, and I suspect it was actually the RAM overheating which caused that.
I put the stock cooler back on it. Currently, it resides in my secondary gaming machine and still works perfectly today.
My previous card was a GF7800GTX, factory-overclocked and watercooled. The GPU never exceeded 40C throughout its entire lifetime, but the RAM was cooled only with ramsinks. These should have been adequate, but I think one of the RAM chips was borderline; it seems to generate twice the heat of all the others.
That card is effectively dead; I can't even play Total Annihilation on it for more than a couple of hours before the RAM overheats and crashes the computer. And because I watercooled it, the warranty was void...
GPUs do not overheat. RAM chips do. If your graphics card is acting strangely, it's far more likely to be RAM to blame than the GPU.