Don - that is a good idea - even better is that you can move the bucket along with you so that the length remaining stays in the warm water. If you removed the whole thing, it'd cool by the time you get to the windshield.
Dishsoap is a pretty slick choice, too. Use a basting brush or old paint brush to put it on. Downside is that your hands get slippery, too & it's tough to hold a tight grip when you need it.
I put my rub rail on while at the campgrounds at our Rathbun event. Left it lying in the sun and worked my way around while having a conversation.