Got me a ATI 5570 last year (low profile for my HTPC). It's a nice little card but it keeps on over heating all the time. I keep getting a nice error "display driver stopped responding and has recovered". I know it's overheating as if I leave a window open with the side (well top) off it doesn't crash. My question to you is are the 3rd party heatsinks at all generic? I ask because I can't find one specifically for my card.
Unless your case is similar to a sealed box with no ventilation or fans or you're running in direct sunlight on the equator, your card should not be running that hot. Download GPUz, get the temperature reading and post it here so we can confirm its a temperature issue.
I use one to keep my GPU cool under load; it sits directly underneath my GPU so it's great for removing heat exhaust, and I haven't had a crash since installing it.
Downside is, that it's a bit loud, especially if you're going for a silent HTPC build; on the other hand my GPU's fan no longer has to rev up to full speed during intense gaming sessions, which can sound like a jet taking off.
Are you overclocking? I have a 5570 that idles at 38c and usually does not go over 55c at load and I'm in Dallas with 80+ temps in the summer even with ac. Sounds like you have a defective card or fan. What brand of card?
If you just want to get an aftermarket cooler than get a zalman vf 900, it is a very compact cooler but is more than enough for the job. It is expensive but I wouldn't recommend it if I wasn't an owner of one. In my personal experience they are very good for this job and only use two slots and also very silent.