I think they will get pretty hot "in a cabinet" if there is no fan, even though CFLs are pretty cool running you still have 188 watts going which can warm up a small enclosed space with no air movement pretty fast. I would say the bulbs should be enough for a small area 20 gallon long fishtank size maybe 30" L x 12" x 12" .
When you buy new twisty CFLs make sure they say 6500K Daylight on them so the plants get a proper spectrum. Usually they are sold in blue packaging with the word DAYLIGHT in large letters and regular soft whites are in yellow packaging. Unscrew one and check the base of the bulbs you have they will generally say either "6500K"(which is Daylight) or "2700K" (which is soft white) somewhere on it.
no expert here but that seems like some potential hot/dry conditions. Correct me if I'm wrong but a 40w cfl = about 150w regular bulb. Having two of those and 2 24w cfl = 75w regular bulbs seems like a lot of light and possibly a lot of heat without proper ventilation. I think pictures of your planned setup would help greatly with members helping you out....
Well regarding the lights so many factors are there. The distance from the plants also matters. which kind of lights are used also matters.Here the intensity of light and the voltage also need to be taken care of.