well i suppose it really comes down to two things:
1) how much of a clean freak you are, and
2) how much of a cooling freak you are
...while a computer is obviously going to stay cleaner when its closed, the same is not necessarily true about internal temps (whether it be the CPU, NB, memory, HDD, or general case temp). with respect to temps, it boils down to the design of the case itself, and you may have to monitor temps both with the case open and closed to figure out which was cools more efficiently. for instance, my work PC cools significantly better with the side on (closed) than it does with the side off (open). this makes sense, as i have a 92mm intake fan at the front, two 80mm exhaust fans at the rear, and a 92mm intake fan on the side that blows straight down on the CPU hsf (which is a stock cooler for an old as hell AMD Althlon 2800+ Barton by the way). I run Einstein@Home 24/7 at 100% CPU usage, and my CPU temps never go above 45°C. this reality is obviously testament to the efficiency of my case in terms of airflow design and cooling capability.
my home office PC on the other hand is based off of an ex-girlfriend's old micro-ATX tower Gateway system. when she gave it to me, i replaced the original Celeron CPU and MSI mobo with a P4 3.2E Prescott and an Intel mobo, but kept and reused pretty much everything else including the case. like the typical mass-produced system build it started out as, its cooling capabilities are severely limited. i have an 80mm exhaust fan at the rear (there isn't room for a larger one), no fan at the front b/c there's no place to mount one, and a Zalman CNPS7000C hsf for the CPU. due to the poor airflow characteristics of the case, it cools MUCH better with the side off (open) than it does with the side on (closed). aside from being a home office PC and performing menial operations and very little multitasking, it also cruches numbers for Einstein@Home like my work PC. and so it is imperative that it has sufficient cooling capabilities. but i also can't stand how quickly the dirt and dust builds up, so my next little project is to cut a hole right above the CPU/cooler in the removable side of the case and add a 92mm intake fan there. hopefully i'll get around to it in the next few weeks...