Please tell us more about your stress test. When you say it "Stops", does it give any errors? If so, what is the error. Does it stop the PC? Or just the test? Maybe some additional info could help us help you.
THe heat sink thermal junction with the IHS will definitely have a relationship to the test stopping. A bubble in the TIM, even if there is enough compound between the IHS and the HSF, can give the same temp results as too little TIM. I had to reseat mine 3 times. The temps didn't change much but now I'm certain that my temps are Vcore related. Call it paranoia.
The Conroe is really fussy about Vcore. A little voltage change will cause a large temp change. Get the best HSF you can. Reseat the HSF as many times as necessary so that you have confidence that it is mounted well. Let the TIM "cure" (I believe this effects temps by 2C-5C, in my experience). For proper curing, get that puppy HOT (up to spec high temp) for about 2-4 hours. Then remove the load and let it run for another 2-4 hours. You'll see the difference.
OK. Sorry for the babble. HTH.