The HP desktop is experiencing unexpected shutdowns after a few hours of use, likely due to overheating, especially since it's located in a poorly ventilated area. To diagnose the issue, users are advised to check the fans for functionality, clean out dust, and consider reapplying thermal paste to the CPU heatsink if the system is old. If the computer shuts down completely without rebooting, it may indicate overheating of the CPU or power supply. Running CPU-intensive tasks can help determine if overheating is the cause. Users should also check BIOS settings for temperature readings, although many older HP systems may not provide this information. If the BIOS lacks temperature monitoring, it may be time for a complete system upgrade, as the hardware is outdated. Free utilities for monitoring CPU temperature include Motherboard Monitor and Everest Home Edition.