I was starting to wonder, with the talk of humid hides and keeping humidity above 50%...certainly isn't right for bearded dragons..but definitely perfect for ball pythons.
For the original question, mesh or screen top covers allow heat and humidity to escape, fast. This typically makes it much more difficult to maintain consistent temperatures inside a cage. How much heat and humidity escape really depend on the conditions outside the cage.
If your house is kept quite cool (via either air conditioner or the climate you live in) it is harder to maintain the correct temperatures in a dragon's cage with a screen top (or screen cages for that matter), which requires higher watt bulbs etc.
A solid top cage with vents on the sides (to promote better air flow) works best as you don't need as high wattage bulbs to raise basking temps and maintain good ambient temperatures in both the cool and hot ends.
If your house is fairly warm, room temperature may be sufficient for ambient temperatures in the cool end, so you will only need a bulb strong enough to heat the basking spot to the correct range. Screen tops still will let alot of heat escape but the cool air from outside the cage won't take much to get warm so less impact.
My room temperature is fairly consistent year around due to having no control over the heat coming into my apartment. Not so important in the fall and spring and during the hottest days of the summer I have Air Conditioner to drop the heat down. All my cages have screen doors infront...which doesn't seem to affect heat loss in the cage as much as a screen top. However, in the winter when its really hot in the apartment because I can't turn down the heat, I tend to open the windows...which cools my dragon's tank sufficiently she brumates. (her cage is on the bottom of the stack) Here the screen doors work against me as it would be easier to keep her cage warmer, if they were plexiglass (though since glass and plexiglass are rather poor at keeping heat in, may not make any difference).
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PHLdyPayne