Yamaha 4 stroke won't start after running at normal temperature

I have a 2006 f150 4 stroke that starts and runs fine until after a run of 30 to 60 minutes, if turned off, won't turn over. The engine will start after allowed to cool for 15 to 20 minutes. The engine seems to be pumping water fine. There's been no overheat alarm. I put a new starter on this engine a month ago because the ignition switch hung up while running and burned up the starter. This happened the first time I ran the boat after buying it so I don't know if this problem existed previous to me owning the boat. Not sure if this is electric or cooling. Any help would be most appreciated.