It depends on the weather...On really hot days, no more then an hour...WITH MISTING and SHADE. On normal days...an hour or more with occasional misting, and shade. (If im letting them sun...Or sometimes if you take your cages out, you can do what is stated below)
My male adult panther is outside most of the time. We have had a wet,humid summer so its perfect. I suspended a feeding cup from a branch and keep a dripper going. The only time he ever gets mad is when i take him inside cause the conditions arent right!!!
Stephen
IMO you still should have a few opportunities to let it bask in the sun. From what I understand it only takes a few hours a week for the chameleon to synthesize the appropriate amount of D3. You could place the cage in a spot where it was partly in the shade. Dense plants create a cooler and more humid environment. You could also consider placing it outside early morning or late afternoon to try to beat the heat. I could also recommend utilizing a dripper/soaker hose above the cage: http://www.mrdrip.com/moisturemaster.htm
You hook it to the spicket and it just continuously and moderately drips water through the tiny pores.
Although I couldn't find it on their site, I believe Walmart carries this hose in smaller sizes for around $8.