I mentioned my HP experience in a previous thread of yours concerning bios upgrades. It was running so hot that it would shut down (ungraciously) doing relatively menial tasks. I'd cleaned the air path and even cut the plastic grilles out to improve things. Bios upgrade cured it completely.
I don't think that there's much point in re-doing the paste. For one, I think that the claims to huge differences is akin to snake oil. Why would a big name brand skimp on fractions of a cent on something important? Secondly - where would the existing paste have gone to? It's still in there. I did a test last summer on an old laptop that I didn't mind frying. Put it together with no paste and compared the indicated temperature. The difference was about 5 degrees and it didn't fry!
One thing that you could do if the bios thing doesn't work is to put an ssd in it - less heat being generated.