Go to the task manager and make sure the CPU is not being used at 100%.
Sometimes spyware installed on a laptop keeps the CPU busy at all times, causing it to produce more heat and having the fans go constantly.
Clean off your computer from unecessary programs. Eliminate unnecessary startup applications.

Joe there is absolutely no problem with hardware, the problem is with youre nvidia Gpu go 6150, amd turion processor runs cool and suprisingly cooler than the nvidia 6150 gpu, prolonged usage with the older bios resulted in overheating of the gpu and often failure, this is a design defect in the nvidia chip itself accepted by Nvidia.
HP couldnot recall all the laptops, so it sort for a temperory solution of a bios update which resulted in cpu fan always on after update, hp is not providing you a solution, the laptop will die on day very soon, bios update will let it live a few months more surpasing its warranty. I suggest you use a extra cooling pad below the notebook, donot bother about the noise the fan makes and the extra cooler will make if you want youre laptop to live a bit long. the cpu temperature will not go pass 40 degrees celsius even if you use it whole day, but the gpu really heats up. The AMD processor is a masterpiece but its been history that heat is always associated with AMD, AMD processor suffer beacuse of some other chip makers fault. donot blame HP or AMD for a failure, it is nvidia. same problem with DV 5000 series with Nvidia graphic on a intel platform.