Honda BF50 Overheat indicator light at higher RPM

I have a Honda BF50 tiller from the mid 2000's I believe. It's always been a great motor. I was out trolling for about two hours yesterday, with zero issues. When I went to come in, and I opened it up, it cut the rpms down, and the temp light was on. As soon as I was back down to idle though the light went back out, and it ran smooth. If I tried to run higher RMP it would cut out, the light would come on, and smooth out at idle. I just came in at lower RPM to get back to shore.

The impeller was changed last season, and it consistently had a good strong stream exiting the motor. I thought maybe the thermostat was bad. I pulled it out when I got home put it in a pot of water on the stove, it started opening in the 140-150 range, looked like it was opening up good, and closed when I put cold water in. I tried it twice to be sure.

Reinstalled the t-stat, ran the motor at the house, pulled out my flir camera, let it run for a while. It seems great at idle, the block and everything was showing like 165-170 external temp on the camera, no indicator lights, the stream was warmer water than the cold hose water going in. I obviously couldn't test it under load at higher rpms though.

I'm wondering what my possible issue is. Maybe the t-stat is opening enough? Like water is moving through the block, but at higher RMPS not enough? I figured I'd try and pick a new one up as they aren't too expensive, and I'm not sure the last time it was done.

Just a note, this is a fresh water only boat, so salt corrosion isn't an issue.

Any ideas would be helpful, thanks!

Just an update for anyone who may find this in the future. I ran the boat without a thermostat as a test, and it still gave me issues. It would idle and go slow fine, but higher RPM's would cause the overheat indicator to come one.
My plan is replace the impeller. It's only a year old, and seems to have a good stream, but maybe it's failing to provide enough water at higher RPMS. I'll follow up with my results.