By check out I first mean make sure it is working.
If it is then look at temperature being reported in the video drivers panel. As it is an ATI card I know there is on in there if you are using the ATI drivers.
Turn it on and then check it out after 10 mins or so. Also after playing an game for 10 mins or so. Obviously before it turns itself off. If it is rising and going into the red then you need to get a bigger fan.
Possibly there is not enough air circulation going on it the case and so more fans may help.
Just re-read you last sentence. If he is overclocking it then that is more than likey the problem. If it isn't overclocked but when it gets slowed down it doesn't turn off (I hope that makes sense) then it is something overheating problably the CPU.
Looks likle either way more fans / bigger fans are needed.
Also could try replacing the ribbon cables for round ones to improve airflow.
Hope something helps there.