I’d love to share my experiences. First, with a screen enclosure, I’d put solid plastic sides on three of the four sides. This can be done with shower curtain or some other water/air tight material. You’ll end up with an open front and top, and three sides that keep humidity in. Second, keep in mind that veileds do really well with nightime humidity near 100%, but daytime humidity that drops into the 30% range. So all you have to worry about is getting your nightime humidity up. Using a fogger at night, combined with over-night misting can easily accomplish this. Temps are pretty easy too. Nightime temps for veileds can drop very low; in fact, it’s good for them. Daytime temps in the mid 70’s (21-25 c) are exactly what we find comfortable, so that’s easy. In fact, the more difficult part is dropping the nightime temps low enough.
As for basking, a lot depends on your setup. The best way to go about it is to have a central basking branch set up so your Cham can get temps of 80-85 (26-30c) for three hours a day, say 9am-noon. Sey up your uvb bulb so that when your Cham goes to bask, he also receives the strongest uvb possible (Uvi 3-6), and you basically have a perfect system.
I know this is a lot of info, so let me break it down into a typical day for your Cham:
Let’s assume your uvb bulb (and other t5’s) turns on at 8 am...:
1) at 8 am, your Cham wakes up after sleeping under a gentle fog from your fogger, and drinks a bunch of water off the leaves because you misted at 7:45. (If you don’t have a fogger, you can mist 4 or 5 times overnight for 10-20 seconds)
2) after hydrating, he heads up to the top of the enclosure just in time for your basking lamp to come on (9am) and sits under the basking lamp, warming up, while getting maximum uvb exposure from your uvb lamp.
3) at noon, his basking lamp goes off, and he spends the rest of his day hanging out, patrolling his territory, and looking for food—moving in and out of uvb exposure.
(if you’re really ambitious, you can provide him a dripper between 2 and 4 pm)
4) his uvb lights (And other t5’s) go off at 8 pm, and the cage gets misted for 10 minutes.
5) around midnight, your fogger turns on, and fogs the enclosure until around 4 am. (Or you start misting sessions of 10-20 seconds four or five times)
6) mist for a good 10 minutes a half hour before lights on
7) rinse and repeat
This is what I consider to be good veiled husbandry, but please consult the others tagged for other important opinions and strategies.