No. I have a reference 4850 with the standard cooler. I do have 3 case quiet Scythe case fans. None of them are very close to my video card.
You can check the temps for the ATI card by loading up the Catalyst Control Center. Go to to last section (I'm not infront of this computer at the moment so I don't remember what it's called). It will display your fan speed and temp. The temp should be under 85C at idle and under 105C at load (IIRC, it will overheat at 110c). Ideally the numbers should be below these temps because they are on the high side.
Note: If your computer is rebooting without playing games then it is unlikely that your graphics card is the issue.
If you think it's your CPU that is overheating but aren't sure then download CoreTemp:
http://www.alcpu.com/CoreTemp/
It's one of the best temperature monitor programs out there. It will usually give you a very accurate reading of your CPU temps.
To give you an idea of what to expect. Your idle temps should be below 50C and your load temps should be below 65C. If it's above 70C then your processor is probably overheating.
To test your CPU and RAM download Prime95:
http://majorgeeks.com/Prime95_d4363.html (This is the x86 one for 32 bit Windows)
Note: This won't test your graphics card. A game is probably best for this although there are graphics card testing programs.
You should run Prime95 for at least 15 minutes to get a good idea of how high your temps can go. If you run it for an hour or two then that gives you the max temps it should get to under normal operations (assuming you don't max out your computer 24/7).
For stability testing you should run this for 12 - 24 hours. When doing this testing it is important to select the "Round off checking" option under advanced. Then run the stress testing by going to Options > Torture Test. Do the "In-place large FFTs" test.