I take it you're related to Rube Goldberg. On the one hand, I admire the
work and thought that went into that, OTOH I think you're nuts. : )
Seems to me there are much easier ways to do that and for what wouldn't
amount to much more money. Personally I just jump into a lake or a river, or
use baby wipes or something if I don't have that option.
I have a picture of me from last year out in the middle of Horseshoe Lake
(elevation 9000 ft.) basically because I'm too cheap to pay $4 for a
five-minute shower. I doubt if that water was more than 50 degrees. TETO.

Cya,
Robert