The two most common failures on cooling failure is either the heatsink falling off or a stuck/broken fan.
If the cooling fell off, you have to find a way to mount it back again. Often, a certain type of pins are used to mount the card. These don't fail that easy, but it happens. I think you can get these mounting pins at about every computer store.
Sometimes, a heatsink is "glued" to the chip to be cooled. This glue can come loose when it gets too hot. Again, the thermal adhesive can be bought at most computerstores.
But what if the fan fails? The fans that are mounted in the heatsinks or most time impossible to replace. Luckily there good cooling sets for pretty low prices available. These sets come with all the materials you need to mount them. A good thing is that most of these sets lower the noise from your AGP card and cool better than standard solutions...!