this is what I did. and have in my garage waiting for the final assembly of the other projects going on right now.
parts I got a radiator with the internal trans cooler built into it. when i bought my replacement radiator it was in there but plugged up. so I got some fittings and some water hose. I had a pump laying around. I got a short section of garden hose as well from an old one. I have a shower head on a collapsing rod from an old telescoping ice scraper,and some wiring. I also have a water valve just like in a sink for hot to cold adjustment. a few tees and some clamps and wiring.
parts list:
Radiator with built in transmission cooler $79 advance auto
12 volt 15gpm pump from northen hydraulics can't remebr what that cost it was purchased a long time ago.
shower head 5 bucks local hardware
valve from an old sink that had a hose connection on it freebie
old garden hose
garden hose repair kit 3 bucks
misc tees clamps and fittings from lowes 16 bucks

here is how I put it together. I have a garden hose with a filter on the end. I have this connected to the inlet side of pump
then I came out of the pump with a fitting and then teed it.
from one side of tee I went to the cold water side of sink valve that I mounted through the radiator support.
from the other side of the tee I went to the radiator trans cooler inlet then went from the tranny cooler exit to the hot water side of the sink control.
from the sink controller it has a standard garden hose connetor on it. to this I attached a short pc of garden hose approx ten feet.
to the other end of the hose I attached a connector to adapt the shower head to the garden hose.
the shower head is attached to the collapseable ice scraper handle with a u bolt.
the ice scraper handle extends out about 4 ft.
I drop it in the short section of tubing mounted to the radiator support extending the shower head about 4ft high from my radiator support.
I then mounted a small section of tubing to mount the handle to the radiator support.
my hot and cold adjustments are inside the hood so I have to lift my hood to use it but
I have to lift the hood to use it any ways because of the radiator support mounted scraper handle.
the shower head is the kind that bolts to a concrete wall with two little tabs and the pipe runs up the wall to it.
I dont have any pics of this but it looks like it will do just fine.
at 15 gpm I should have plenty of pressure and can control that with the valves.
if it gets too cold I just close the cold side increasing the flow through the hot side. and vise a versa
I can even just pump cold water if wanted.
I also was worried about water in the lines during freezes so I got another fitting to attach an air line quick connect to the system and blow all the water out of it.
I just open the vlve turn on the pump and hook up the hose.
I also have a bed mounted water tank that holds seven gallons of fresh water. I got that from a old cubby cabin boat.
when I had drum brakes in the rear I thought about running a line down to each of them to wash them out after the mud.
but went to disk brakes instead.
I hope this helps
I have electric fans on the radiator that are thermostatically controlled to kick on and off at 180 degrees. so it should stay pretty hot.

I also thought about the water not heating up fast enough to be useable, so I have plans if the first set up doesn't work, to run the hot line from the radiator to the tank in the bed and just put in a tee before the pump to pull from the tank letting it circulate until it is hot. then I have seven gallons to shower with along with the cold water flow.

and with what your talking about doing the dual lines one cold one hot teed from the pum would allow you to set it as hot as you want. even slightly warm water is better than nothing. they use what you are talking about in ski boats as well for water skier to warm up their wet suit before jumping into the cold water. they even work as a shower to warm up with after skiing in cold water.

a 12 volt pump
a switch with relay
an exchanger
two line for fresh water
two lines for radiator hook up on the hot outlet of the water pump
a shower head
and a set of valves.

now my brain is tired