Unusual overheating problem, tried everything! 60 2 stroke

[Islandfisher88]

Hi, I'm experiencing an overheating problem with my Yamaha 60 2 stroke outboard. I've tried pretty much everything from the list of basics but cant find the problem.
The impellor was new 6 months ago and upon checking looks good, also the water pump assembly in general looks ok.
I've already removed the Cylinder head cover and cleaned all deposits
The exhaust outer cover has also been removed and all deposits cleaned
New thermostat, checked in a pan of hot water to make sure that it works
New thermo switch (I replaced this when tracking down an intermittent overheat alarm previously which turned out to be a nick in the wire between the switch and the electrothermal valve)
No obstructions between the water intake and pump
The engine's been running fine up until last saturday when after a brief run at lowish revs I switched it off to allow friends to get onto the boat from the water. When I went to switch it on the overheat alarm sounded. Now the engine will be fine when first turned on, fine when at high or highish revs but after about a minute of idle the alarm will sound again.
Tell tail is pretty strong, cold or warm when running at speed but very hot when returning to idle.
Any thoughts would be appreciated,
Thanks

[Bluefish]

Have you check the pressure relief valve? And I’ll just say on an old Evinrude I found salt deposit in one of the temp sending unit cavity that was causing and overheat alarm

[ausnoelm]

Has the entire water pump been replaced or just the impeller? and were genuine parts used?