easy solution.

2-liter soda bottle. filled with water, bungeed to your rear rack.
most racks have a black platform. if not, a black piece o' plastic under the bottle
to help warm the water. or paint the bottle black. whatever.

end of the ride, you have hot/warm water.

you brought extra soda bottle caps right? of course you did. now take one of
your sewing needles, warm the tip in the flame of your lighter. poke the hot
needle through the top of one of the extra bottle caps. repeat about 15 times.
now change bottle caps. crikey! you gots a hot water sqeezie-shower!