1.Sounds like a PSU malfunction, higher temperatures would mean the fan would spin faster therefore more PWM(Pulse Width Modulation)requirement and that would mean more voltage being taken from the socket and passing through the PSU.
2.Or it could be the power cables being faulty.
Should be either option, if not then I don't really know, get a computer enthusiast to review the PC.
EDIT:
(01-04-2016, 05:56 PM)Antonio Wrote: Maybe the fan is not working properly, causing it to overheat and shut down to prevent damage?
That can also be the source of problem, install SpeedFan and monitor the temperature to see if it goes ~90c or more.
EDIT2:
(01-04-2016, 05:51 PM)Snoopy Wrote: 2) We've had reports that it could be the power supply yet the manufacture (When it was brought) said it's fine. 650Ws. Is there any way we can test this without buying a better power supply?
As I've said above, monitor the temperatures and see if the PC shuts down at a specific temperature, if it does, swap out the PSU and check again if the PC shuts down after reaching that specific temperature. Sadly that's probably the only way to know if a PSU is faulty(there might be some other way hidden somewhere deep in ye olde archives)