A very odd problem indeed - As you stated, most machines these days have failsafe devices to stop your PC overheating and in most cases will either beep to warn you or simply shut the machine down. Additionally, many power supplies have internal fuses that can trip out to protect the machine should there be any power surges.

Your first bet would be to clean your machine out paying particular attention to the PSU. Under NO circumstances should you open the PSU itself - It houses capacitors holding lethal amounts of charge long after you shut down the machine - But what you can do is take a can of compressed air to the fans and surrounding grills. It seems unlikely, but it's worth trying just to check that there isn't a build up causing problems with the power supply.

Other than that I can only really suggest checking the circuit breaker itself and replacing the PSU. Faulty PSU's can cause many problems, and whilst most concern the PC itself, it's not impossible for it to be causing a problem externally.

One other thing - Have you added anymore hardware to that outlet recently? I suppose it could be possible that you are drawing too larger current from the outlet, particularly when your PC is under load or if you are using other devices in addition. That would account for the circuit breaker tripping, though only really makes sense if you've upped your power demands recently.