Those compartments are essentially a wet/dry filtration system. Personally, I don't recommend wet/dry systems for a reef, since they tend to load up with a lot of organic material and only add to potential nutrient problems. You could probably still circulate water through it, and hide your heater in there anyway.
Somebody else may have a better suggestion.
As far as lighting goes, you can just leave it off during the cycle... leaving it on (or even having it on) will only supply algaes that will be trying to grow with much-needed light, and then you'll have a lot of nuisance algae to deal with. It's better to leave it off until the cycle ends and nutrient levels drop, so that their primary source of food is eliminated... then you can turn on the lights once you start adding in critters.
Good luck.
