There is a lot of bad/confusing/contradictory information in this thread. Just for clarification, the 4TEC engines have two separate cooling systems. The engine itself is closed-loop cooled, using antifreeze, with the ride-plate used as the heat-exchanger to the water. It takes a pretty long time running our of the water before the engine will overheat. The second cooling system is the exhaust ( and intercooler on SC models) cooling system which is open-loop, fed by the jet pump while in-water, and the hose port when out of water. Unlike the engine, if you don't feed water to this system, it will overheat the exhaust system in a matter of seconds, not minutes as others have implied.
Separate is the carbon seal, which shouldn't be run out of water without cooling for more than maybe 5 minutes.
I have run 4tecs out of water for a much longer time, up to an hour, by simply rigging up a hose spray to spray both the ride plate and carbon seal from below. I use this setup to run the engine in the fall even for a 5 minute run before changing oil, as I personally don't like running for any length of time without cooling the carbon seal.(for this purpose, I don't spray the ride plate as I want it to warm up fast.)
As a side note, the new 1603 ACE engine in the 300HP skis has another open-loop engine heat exchanger.