I would say no. When the computer is turned off there is a small amount of power still supplied to the motherboard but its so small I can't see how the power supply would be warm, perhaps someone else can comment better on this.
I would say this is ok - the psu still has mains current going into it even if the pc is switched off - unless the psu has a switch fitted to isolate it and this is turned off. This current will cause the transformewr to become warm.
Computers run fairly hot and the fans keep the temperature from roasting the board, graphics card etc. When you turn off the computer the fans stop straight away but the heat will still be inside for longer and there are no fans to cool it.