From what i've read, you have already determined that the fans and other essential parts are in working order. I'm going to go under the assumption that the thermal compound on your CPU is not functioning properly, which commonly happens over time. This should be an easy matter to fix, there should be info on the HP website of how to re-apply it. If you have any questions, I would be happy to help you out.
This article should really help you out. Thats not your exact laptop, but they are extremely similar.
Though I'm quite sure that the problem is originating from the thermal compound, make sure to double check your fans and heatsink before undertaking the process of reapplying the paste. Try to find more information on your particular model, and if you can, gain visual access to your CPU, the paste should not be hard to identify.