Welcome! If you make some quick changes and do a lot of misting I bet he'll be just fine.
Here is my basic checklist for a baby veiled:
-a screen cage of appropriate size (baby:16x16x30, adult female 18x18x36, adult male 24x24x48) you can also buy the adult sized cage and just section off the bottom so it is smaller
-live plants that are non toxic and have covered organic fertilizer free soil
-a normal incandescent house bulb of appropriate wattage
-a dome to put the house bulb in
-a linear reptisun 5.0 and appropriate hood
-a digital thermometer or temp gun to check temperature
-a digital hygrometer to check humidity (you can buy a 2 in 1 thermometer/hygrometer)
-three supplements: calcium with d3, calcium without d3, and a multivitamin that contains no vit A (make sure all are phos free)
-a pump style spray bottle to spray chameleon
-a dripper of some sort
-drainage for the water so that the cage does not flood
-many horizontal, vertical, and diagonal branches/vines/perches make sure there are many at different levels under the basking branch so he can move around under them to get a certain temp, the closest one to the bulb (6-8 inches under it) should have the maximum temperature a baby veiled can handle (80-83 degrees)
All of this can be bought on lllreptile.com but it would be cheaper to buy the uvb hood, normal incandescent house bulb and dome, plants, and digital thermometer from home depot or lowes (unless you are getting a temp gun, then tempgun.com) Veiled chameleons can handle temps as low as 50 degrees (at night) so there is no need to use a night light, though I would try to keep it around 60 for a baby. If you do need extra heat, use a space heater or ceramic bulb.