Whenever plants are "wilting", that is an indication that they are transpiring (sweating) faster than the roots are keeping them hydrated. There is absolutely nothing wrong with giving your plants a "foliar drink" when they show this stress. Much like a cool drink or wipe-down for us, during extremely hot conditions, will cool AND help re-hydrate us. Pepper plants can "drink" through their leaves. Wilting is a perfect indication that a foliar mist/drink is a good idea.
The primary goal with misting though, is to bring the surrounding temperature down. In this case, the evaporating mist, AS IT IS EVAPORATING, is lowering the temperature in the shade-house. Plus, the effect of the actual foliar drink (if any water droplets make it to the leaf surfaces) is also beneficial when wilting is taking place .
PepperDaddler, misting will absolutely help you. The further away from 100% humidity the air is, the more cooling-effect you will get from misting.