Javrak gave you some excellent suggestions above.
Seagate tools: try running the long test (as opposed to the short test) for HD integrity verification. If you are getting any failure notices from Sea Tools, better replace the HDD pronto or risk losing your data. Running the test over and over for an hour will not help, a single pass will give all the information you need.
HDD: the hard disk is not causing an overheating problem. By running it constantly for long periods the HDD itself may overheat, but that won't cause the entire unit to overheat. Your problem is elsewhere.
You need to verify exactly what temps the unit is running at, otherwise you are just guessing. How do you know it's overheating? As Javrak said above, use a (free) temperature monitoring device to get verified temps. Here is another I keep on my flash drive "toolbox": leave it open in your system tray and check the temps occasionally as you use the laptop to get accurate temp readings.
Please post back with results.
Note that if your client is trying to game with this unit, it really is not intended for stress-applications. This is a little e-mail and web-surfing unit, not intended for extreme applications.