Even with just having the unit turned on for less than 5 minutes, the monitor will pop a message that the PSP3 unit has grown hot and needs to be shut down. We recently bought this unit just a month ago. What could be the reason behind this? Our place is airconditioned and we make sure that the unit is placed in a cool place and not cramped which may cause overheat.

NOT at all normal.

Sounds like you have some dust bunnies blocking the air vents.
Time to get some canned air and blow ALL of the exhaust post out.