There should be no danger of putting a normal compact fluorescent in a tri-light socket...but they do make CFL's specifically for tri-lights and dimmers. I've got a normal CFL in my tri-light and it's been there for years and hasn't given me any problems.
A regular tri-light bulb has 2 filaments, on low one filament is on, medium other filament is on, and on high both filaments are on. If you look in the socket you will see an extra "pin" between the center point of the socket and the threads that the lamp screws in to...this pin supplies power to the 2nd filament.
This link has some good info on CFL's: http://oee.nrcan.gc.ca/energystar/english/consumers/questions-answers.cfm?attr=4