Continued:

Troubleshooting my Yamaha wave runner FX140 WR1000AC running hot 4 stroke engine
(may apply to some 2 stroke skis as well)

If the engine is running ok on the hose but not in the water may be a water flow problem.

Pee holes / Tell Tales / water hole on side of hull check

Pee hole /tell tale on left some water cones out when you rev it on hose, at ramp did not see anything (?) lower revs
Pee hole / tell tale on right no water comes out on hose
I heard right pee hole was a pressure relief for the thermostat so some slight water with steam may come out while underway. I did not have steam coming out of my right tell tale

Checking the temperature sensors

You have three temperature sensors, two are for overheating safety and one is for the engine fuel injection system to get proper fuel air mixture for the fuel injection system.

The safety high temperature sensors (one on the exhaust and one on the engine) turns on the overheat light and beeper and puts the engine in a limp home mode and will drop the rpms so you can go slow in and or shut off the engine .

When the high temperature light comes on you can disconnect the exhaust and or the engine temperature sensor where it plugs in at .
 If the alarm goes away either
1- the sensor is bad or
2-you are overheating your exhaust possibly lack of cooling water.

Suggest that you use an infrared thermometer to see what the actual temperature of the exhaust or engine is, disconnecting the sensor if you have a problem could cause serious damage to the motor or exhaust system

You can check the sensor by removing it and putting it in a pan of boiling water and monitoring when it turns off and on by temperature the procedure is in the Yamaha technical manual
it will read open until it gets to the high temperature then it will close (normally open)

Cleaning salt deposits out of engine

*(Ideally if I find the blockage would take it apart and clean it) and I use salt away or joy dish soap from time to time but...

 Doing some research on cleaning out salt deposits using vinegar mixed with water.
 Some people put their outboard in a bucket with several gallons of vinegar and water and run the motor to flush out the salt corrosion  then flush out the vinegar mix
OR use a pump with a bucket to circulate the vinegar solution into the motor and back into a bucket.

 Went to Costco got some vinegar and going to first try soaking it marinade the beast may try the pump with the bucket to circulate the mix...that's if back flush does not work or flush out after soaking it

Caution Do not be tempted to use muriatic acid or HCI will eat rubber and everything else

I called the South Seas Yamaha dealer here yesterday and they said "one month wait for diagnostic check"  $140

ordered the YDS  Yamaha Diagnostic System software and cable yesterday $70 and I have the factory manual but not much about cooling troubleshooting in there