Well as long as you register it as "hot but not too bad to hold" (which I gather is at ~40 degrees Celsius or in English: a good hot bath temperature) your PC should not suffer from that too badly.

However that funny thing with your power supply is rather more worrisome.

If you can't get to POST screens something is seriously not good with your PC (disconnected, burnt out, crucial pieces of hardware not coming online properly, or otherwise not OK); if you have intermittent powerfailures it suggest the culprit is either in the power regulating circuits of some component (very bad) or the battery (bad but replace-able).