Unfortunately, we don't have any suggestions of what can be done to approach HP about this. One of our techs has seen a lot of these issues with this particular machine. The problem is a faulty design: some designer put the heating vent on the bottom of the machine, where the ventilation is going to be pretty ineffective.
The tech's idea...put it on a book. No, seriously. Elevate it so that the vent in the back can get some space, and therefore some air. (Yeah, it's about as low-tech as you can get, but the tech swears by it - says three friends have had the same problem, and that this is what works for them.)
Sorry you've had so many problems with this particular unit. We're HP authorized, but obviously we're not HP, so we can't really do anything about this particular design.