Traveling with dogs

So we're planning on taking a three week car trip this summer, and we want to take Zeus with us. We'll be doing pet friendly hotels and campgrounds, and we'll be OK at the National Parks, but we're wondering what people do with their pets when they want to go to museums and other indoor places.

It will be too warm to keep Zeus in the car, since the temps will be in the 80's. We were thinking of just taking his crate and putting him in his crate outside somewhere, but I don't know if he'll get too hot in there, and shade isn't guaranteed. I know people travel with pets all the time, so this can't be an unusual problem. Any ideas?