I do something similar by heating up the entire content of my trailer fresh water supply with an Ecotemp water heater. I basically take the shower head off, then stick it into the fresh water tank inlet (large opening). The water recircs and heats up while I do other stuff like setup shower tent or cook. After five to ten min, the EcoTemp unit is turned off and the water keeps recircing through it until we're ready to shower. At that time, I screw the shower head back on to the end of the hose and shower like normal. The shower head has a on/off toggle thing.
This eliminates the cold water followed by scalding water issue you get when you use the EcoTemp as an "on demand" water heater. Getting the water to the right temp tends to waste a lot of water this way. The down side is that heating up 10 or more gallons of water can take time and burn propane. I have a ten pound bottle so this isn't a worry for me. Another up side to this is that the warm water in the water tank is nice to wash our faces with on the following morning. My tanks are insulated with 1/2" foam so the water isn't frigid for your face first thing in the morning.
To be honest, I'm thinking of going the way of KISS rule and just using a solar shower and a gravity feed system. I can still use the EcoTemp to heat up two gallons of water, mix it with one gal of cold water and fill up a solar shower bag. Then hang the bag up high or on the shower tent hook deal and use it. The user has a consistent water temp and don't have to deal with water temp or water wasting issues nor do I have to worry about going through as much propane. The down side is that the following morning face washing will not be pleasant!