Hot tub technician offers input:
I'm assuming this walk-in is in a bedroom and you normally keep the closet door open but must lock the closet door when you leave...???
I'm also assuming you can't cut a four inch hole in the drywall somewhere and vent to an attic, crawlspace or the bedroom.
You could use water to cool the tent but the best way is to build a simple heat exchanger. You must exchange the heat from one space into another.
Anything you do with an open tub of water requires evaporation to dissipate the heat. Evaporation inside the closet will just add humidity to the equation and compound the heating effect. A large, closed body of water might act as a 'heat sink' but it would only work temporarily until the tank of water was the same temperature as the tent.
Building a simple heat exchanger:
Place a long coil of (ideally) copper pipe on the ceiling or around the walls in the top of the closet. Place another coil of copper pipe outside the closet. Connect the two with a small circulation pump and fill the system with water.
The coil inside the closet will absorb heat. The coil outside the closet will dissipate the heat IF the the outside space is cooler AND if you use a fan to blow heat away.
Either way, you need to move the heat somewhere outside the closet or it will be like opening the refrigerator door to cool the kitchen.
If you can put the discharge coil in the bedroom it will transfer the excess heat from the tent/closet space into the bedroom.
I found this on the Internet to give you some idea of what I'm describing... You could even use this gizmo to help heat the bedroom in winter (effectively for free) if you live in a colder climate.