My Veiled also runs/dodges the water most of the time, then sometimes he will sit there and enjoy it.
I normally just mist spray the plants etc to increase humidity etc and if its very hot ill give him a few sprays until he is just about to move away. They like warm water. I also use a filter on my tap as i noticed a white build up on the plants.
I run the tap till the water is very hot, fill up the spray bottle and test it by spraying it on my arm, because normally by the time the water hits the cham its warm. my spary bottle has a very fine spray.
I have a dripper in my cage, most of the time when he wants to cool down he will go sit under the dripper and the drops will run down his sides etc.
Thats one thing they hate is cold water he he, and trust me veileds can move like lighting when they want to.
But if its uber hot and his mouth hangs open he will take the cold hose water for a few seconds.
I never leave my cham's outside in the sun with out checking up on them every few min. Leaving them in the sun with out a little shade will toast them in the South African heat. One way to see if they are getting to hot when they are outside is when they turn a very light color with there mouths slightly open.
ROFL!! no i think it is because they are cold blooded and the cold water is a shock to the system.... But when my chameleons are outside i use the cold water hose to mist the flex, he will run for cover somewhere in his umbrella tree (Schefflera) and drink and what not.
My veil does not like mistings and will run away but my amibole just sits there and takes it. The odd thing is that my veil is mellow and is easily handled and the amibole is a mean bugger. I'm guessing its a personality thing.
My herp vet gave me a great solution: Go buy a large mister at the hardware store - the kind you use on a large area. It mists a very fine mist... then fill it with the hottest water from the tap you can. Once you mist the cham with it, the tiny droplets will be just the right temp. Always test it first - mine is never too hot. I start misting the plants and cage first, then work toward my cham. I try to go over her head so it falls like rain. She usually runs at first, but usually always stops and sits for a bottle. Sometimes she will take two full bottles! There are always those days that she wants nothing to do with it, but if you mist daily, these are few. Good luck!