"just clean up the old thermal compound from my cpu and heatsink and put new thermal compound on it."
Why is it everyone immediately suspects the TIM? I would first suspect the fan isn't spinning, which is easy to test for. If spinning, my second suspicion since it is an older system would be dust. I've seen heatsinks with so much dust in it that after the fan was removed, the dust could be peeled off like the lint in a clothes dryer.
I've seen posts about people getting magical results after removing the HSF and reapplying TIM on an old computer, and invariably (if they admit it) they would mention that while they were at it, they also blew the dust out of the heatsink.
Yet the results
must have been the new TIM.
I had a laptop that did that to me, finally realized the thermal pad that DELL used had literally fallen apart such that the laptop HSF was no longer making contact with the die.
That's because it was a pad, not a thin layer of the typical thermal compound.
DELL laptop, warranty is worthless the day you press the "purchase" button on their website.
YMMV. I've had two good experiences with Dell warranty service in the past few months. Yes, they will want to run through troubleshooting, but in my case "He's dead, Jim." Won't power on even with a different AC adapter and battery from a second, identical unit. Because my warranty was for depot repair and not on-site, Dell mailed me a pre-paid shipping box. I received the fixed notebook less than a week after I shipped it.
What's worthless is the fact that the second, identical notebook also failed in a similar manner. D: Both failed just before the 1 year warranty was up. I've never had another Dell notebook fail me (so far) and I've owned many. So, avoid the Inspiron Mini 1012 netbook.
I had sold my second, working unit to someone and it died on them, not me. They had a similar experience with getting it easily repaired under warranty. Since warranty just ran out on both I gave them the one I still had, for free, just in case it dies again.