Second thought. The cold water is routed to the bottom of the hot water tank through a dip tube. The air connected to the cold water inlet port would rise to the top in the tank and exit through the sprinkler head I think.
Connect the air to the hot connection, and the cold connection to the sprinkler head?
Sorry; the dip tube would be removed prior to using the tank for this purpose. The hot water pipe picks up from the bottom in my proposal and no heating elements need be incorporated.
This is basically an oversized version of the old-fashioned water-filled hand-held fire extinguishers Class A.
The difference here is the secondary pressure tank to fully flood the fire in less than five minutes.
An 80 cubic foot room measures 10 feet on a side and 8 feet high; an inch of water on the floor is about 63.5 gallons.