It does sound like the laptop may be overheating.
Make sure you are running it on a hard surface and that the vents are not blocked.
As this is an HP i7, does it have the HP utility that runs the fans up to their highest speed to try to blow the dust out? Can't remember what it is called but I know that HP ship that as part of their toolset.
Also, manually inspect all of the vents to see if any are blocked.
Also make sure that you have not used a utility to restrict the fan speeds to make things quieter. An i7 is a VERY powerful CPU and will generate a lot of heat when running hard. So also ensure that you don't have something running that is driving up the CPU levels. Have a look in task manager - if the CPU is continually running over 10% without any other applications loaded, something needs to be uninstalled. My i5 laptop is running at 3-6% with several firefox windows and task manager running plus a load of background apps that are largely inactive just now.
You could also try running a Linux boot disk to see if that makes a difference - you can download them and burn onto a CD/DVD that you can then boot from. That will tell you if it is some problem in Windows. If it is, you might need to reinstall Windows or at least clear out all those old apps that tend to accumulate. If it still happens, it is very likely to be a hardware fault that will need a specialist to look at.