This sounds to me like he has took out the battery to gain access to the sim without turning off the N900, what is not clear is how the device got so hot if he put aside the battery or maybe he put the battery back in and it got hot as the device tried to turn on, holding the phone on the AC he means air conditioning which brough it back down in temprature.

Very unwise and should never be done to just take out a battery before turning off the device and especially if some programmes are still active and running, it is the same as a pc which could in effect totally screw up the operating system hence why he may well need a reflash to put it right.