Either keep the case closed and buy another fan for the back of your case (in order to create a directional flow of air through your case), or just keep the side door open and keep your house fan pointed toward the case.
It's a micro. Not much you can do with it to cool it other than get a can of air and clean it really good.
Also if it's one made in 2005, it could be the thermal paste has dried out and needs to be replaced.
OK ok ok Different documents on the Dell site have different size info for the gx620.
One refers to 3 different versions of the gx620 and another refers to the micro only with no mention of the other version. So it does come in a tower version.
I've had some Dell's before and this comes to mind >
When you open the side is there a green or black plastic hood over the cpu heat sink that leads to the fan mounted on the case? It's a dust magnet. If you remove the hood I'd bet real money the heat sink is clogged up pretty bad.
The way the hood and fan are married in those sort of systems you can't leave the hood off. It's the only source of cooling for the cpu. Now I like to mod. So on one of the systems I had I took the hood off and screwed down a fan blowing in to the heat sink. Then plugged that fan in to the cpu fan header. The big fan got moved to the back blowing out of the case and plugged in to the case fan header on the mother board. Worked great.
You can get dirt cheap fans from a small computer shop for next to nothing.