My FIL recently bought this little boat off a guy and is letting me mess with it for the time being. It's a 2013 25 hp yamaha 4 stroke. Very, very clean engine. Only thing is that it won't pump water until 4-5 seconds after I start the engine and stream is pretty puny. Also, water is a little on the warm side at idle on the ear muffs. I'm not going to take it out, much less run it WOT til it gets tuned up.

Any idea what it might be?

Can’t hurt. Just consider it your annual replacement.

Just replace the impellar once a year and ur good to go

From what I have seen after owning three 4-strokes is that the stream isn’t as hard as I was used to on a 2-stroke. With that being said, I would change the impellar just to be safe since you don’t know when it was done last

Mines an 2003 model Yamaha 25hp 4 stroke idling in the lake it puts out a weak stream compared to my buddy's 25hp mercury 2 stroke but its solid and steady. I put a new one in mine once a year for piece of mind. One year I didn't do it drove 1.5hrs away put the boat in with my brother everything was good it was putting out water so he parked the truck and I went to dock and shut the boat off till he got to the dock. He got in the boat and I fired it back up and we had no water coming out we couldn't find any one local that had a water pump after we figured out what had happened so we had a whole day of hunting ruined and had to drive an 1.5 hrs back home because of a 13 dollar part and I didn't replace it that year. Now I keep a brand new spare in the boat with the wrenchs needed to change it

Your not supposed to run Yamaha’s on ear muffs without removing the inlet screens first due to the angle of the water pickup in the inlet screens. It will damage the impeller. 4 strokes run the same water pressure as a two stroke, but pee a little weaker to due water routing.

I was running it at idle for a couple minutes. It was pumping water but not super strong. Could that have messed up anything besides the impeller?

I once had a Suzuki that was thermostat controlled. It allowed the engine to get up to operating temp before it would pump water. There was always a slight delay after cranking cold. That may not be your problem though and changing the impeller couldn't hurt.

Take a piece of weed whacker line and run it up the pee hole while the motor is on. I do this about once every 4 trips and it makes a huge difference in what you see coming out. I've read (don't know the validity) that some streams are just indicators that the impeller is running so the temp of the pee doesn't really matter on those models.

Yes, replace it.

Doubt it. At the worst case probably just the impeller and the housing. You have to remember, an outboard gets the hottest at idle. No blowing air around it and pure heat circulating around in the engine cowling.