download speedfan,, just search for it on google. That will allow you to monitor the temps. Also get baseline temps to compare to, i don't know what the normal temps are for your processor.
my experience is that closed in cabinets are bad.. a computer needs circulation to survive, without it, you are only recycling the hot air, and not the ambient temperature of the room.
what i would do if you really want it in that cabinet is to mod in some fans in the door and rear if you have the know how. large, low rpm fans would be practically noiseless and would give you a bit better circulation