The 24" imac's "graphics card", if you want to call it that, is an odd looking thing. It's a very small board (under 3"x3") with an edge connector that looks very much like a sodimm. from there are heat pipes that extend out at an angle for quite a distance and then meet the radiator.
These two are provided by apple as a single unit, but the design allows the GPU to be replaced/changed without replacing the logic board, which is unusual for an imac. (I'm a little surprised I haven't seen any upgrades available from 3rd parties yet, but I bet we will, eventually)
Because of this, the GPU is never separated from its heat block when serviced. In MOST cases with Apple, chips on heat sinks that are not meant to be taken apart don't use heat sink compound. They use a thermal tab or pad of varying types instead, some of which are glued down to the die and block/spreader. It would not surprise me if the 24" GPU does not use heat sink compound.
Puting that aside for the moment, it's extremely unusual for heat sink compound to dry out, because it's usually smashed under fairly high pressure between the two, with an almost zero-width gap to try to wick air from, and there's excess compound right outside the gap. The purpose of the compound is to span paper-thin gaps in the unequal surfaces between the die and the spreader, which are usually already nearly perfect. Heat sink compound doesn't dry out for the same reason that a wet piece of paper would never dry out if set on the kitchen counter under a flat bottomed plate.
I periodically run into people complaining about Apple applying too much compound which only makes me laugh. Considering the screws that crank down the die, you could dump a few tablespoons of the stuff on the chip before fastening it down and all you'd accomplish is the excess would all squirt out the sides, but the resulting gap would be the same.
Because this process relies on there being too much compound to start with, and presses out the excess, you CANNOT separate them and then reassemble without removing the old compound and adding new. Once you press them together, you go from having too much to having just enough, and then if you separate and reassemble them, you go from having just enough to having almost enough. (and possibly an air bubble/gap) The other possible compound issue is if there's a bubble in the compound. Properly applied compound is placed in a single, bubble-free blob in the middle before assembly, which makes it impossible to get a bubble of no compound between die and block.
Which brings us to the real issue, heat. Temperature changes make things expand, and different materials expand at different rates, and conduct heat differently. If a connection is bad, it can still work. Like two wires in an electronic device that are merely touching but not properly twisted or soldered together. But if subject to vibration, the wires make and break contact and you have a problem. With small things like bonding wires in GPUs, it's not vibration that causes movement, it's heat. So if there's a defect, it may not cause problems until heated. Thus, keeping it cool can delay or mask the problem. This is probably what you're experiencing. Note that this is a problem either inside the GPU itself, or due to the mounting of the GPU to the card, and is likely caused by a GPU manufacturing problem or a GPU manufacturer's specification problem. A good example of a specification defect recently is the
Macbook Pro Nvidia Defect. In that case, Nvidia specified lower cooling needs than were actually required, leading to the GPU being damaged by its own heat production. (actually the GPU's attachment to the board is failing due the thermal stress)
I've seen a few 24" imacs with problems similar to yours, I replaced a grapghics card yesterday actually for this, and it would not surprise me if it's the same issue. The GPU makers are competing for customers, and lower heat production is a major selling point, which encourages them to fudge their numbers to get sales, which leads to defective or higher-than-acceptable field-failures in end-products like the imac. With the MBP/8600 issue, it's interesting to note that after the defect was discovered publicly, Nvidia "researched" the problem and notified Apple that none of the chips they bought were affected. Apple got tired of all the repairs and launched their own independent investigation, and found that a small number of the chips were indeed affected, and extended coverage for some of those machines out of their own pocket. It's possible we may see something like this for the new imacs later down the road. Apple typically waits for those machines to fall out of factory (1yr) warranty before announcing repair extension programs.