Hello Bronn,
Welcome to the HP Forums!
I understand the computer has an overheating issue. Since the issue was still present before upgrading to Windows 8.1, I would ensure you have attempted everything in this document: Reducing Heat Inside the PC to Prevent Overheating
If these steps do not help, I would contact HP phone support to get the product serviced. You can utilize this website to learn how to contact HP appropriately, based on your region: Contact HP Worldwide
Please let me know if you have any other questions or concerns. Thanks!
Mario