Dont know about the heating issues, maybe. However there will be less resistance on the prop and you will get an inaccuriate result. Also, you never really run an electric at a constant speed or for a solid block of time. If you really want to test it, I'd suggest take it out and use it for a full day and see how it goes. You could run it in a garbage bin if you want, with a bit of splashing.
I take it you dont have a battery system on your outboard. Another option is a dual battery system for it like on a 4wd. Then you'll never have a problem.