Assuming theres not a sharp drop in temperature overnight and the enclosure dries out
I cant see it doing harm, but it dosent sound very effective either.
When you say 80's and 90's do you mean ambient temp hits that throughout the cage? no cooler spots?
That is getting a little warm for a young veiled like yours from all accounts, but equally people say veileds can tolerate a fair varience in temp. That said, its ambient temp and due your current weather, aka constant (whats it like in the day?) then I would personally seek to rectify that more permanantly.
Simplest would probly be cooling the room its in, by use of a AC or fan (but no draughts on the cham directly) if possible. To my thinking, it would handle such temp varience better if you afforded it better ventilation in your climate, Aka a screen cage.
Larger caging may also assist (better thermal gradient, heat rises, cooler near floor) (*bare in mind, not so large your cham cant find its food)
Glass tends to hold ambient warmth in warm climates. Sometimes cooling can be as big an issue as warmth with reptiles. I have similar difficulties here in summer, my turtles find themselves swimming with frozen water bottles! (still in tanks).
Barring the above suggestions, perhaps adding another leafy (safe) plant, and misting that during the evening (if you can do so without disturbing the sleeping lizard) may help,
air cooling via water evaporation, but again its probly an inefficient means. Barring a screen cage,
Cooling the room itself if you can is probly most efficent.
Note: This is just my opinion, formed from personal hands on experience with my own young veiled last summer, Im sure somebody wont like it and will have a tantrum, but what can you do.
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