Ways to prevent overheating on XBOX 360?

Assuming it is overheating, and before spending money on an external device, see if the tips Microsoft provides about placement of your Xbox help:

• Put the console in an open area with lots of ventilation. Do not put the console in an enclosed space.
• Do not stack other electronic devices on top of, underneath, or against the sides of your console.
• Make sure the console and its power supply are on a hard, steady surface. Do not put the console on anything soft (such as a bed, sofa, or rug).
• Position the console away from heat sources, such as ventilation openings on televisions and electronic devices. Also, keep the console away from heating vents and direct sunlight.
• Position the console away from high-vibrating sources, such as low frequency speakers, subwoofers, etc.

And whatever you do, absolutely do not place your Xbox next to a picture of Clippy:

I really recommend to get some ventilation room for the xbox. Setting up internal fan is hard and external fan may not help that much. And as you said, it can make the problem worse.