If it is a CRT, and it is actually overheating, and the vents are not obstructed, unplug it, and face the fact you will be replacing it. Repair is usually not cost effective these days on a CRT unless it is a really expensive or special model. And an overheating monitor can catch fire very easily. DO NOT open it or mess with it yourself. As Wulf says, there is a capacitor in all CRT models and it can hold enough charge to kill you (literally) for a LONG time after it has been unplugged.
If it is a flat panel monitor, LCD or TFT, it might have some warranty left on it depending on how old it is, and if it has an external A/C adaptor that seems to be the part that is overheating, you can replace those sometimes, and the monitor is fine.
-Skylark