JET 737 DISHER WASHER. IT STARTS TO WASH THEN IT STOP TILL YOU PUSH START . HAS OR ON RINSE TEMP.

You may have a leaking hot water electrovalve, replace it.

The reason the temperature are going up is the heating system is defective. The thermostat on the booster (rinse) is not satisfied. First thing to verify is the contactor that is activated by the rinse thermostat. Often one of the wires on the contactor will burn.

If the machine will fill on its own when it is empty then the rinse cam on the timer is defective

Please be carful as running the agitator without enough water will overheat and kick out the motor, however it should be ok when it resets itself.
Yes, the machine should stop agitating when you lift the lid so this too is part of the problem.
After looking at the print I can only suggest that the cam contacts in the timer ( contacts 12 and 14) that start the motor are burned and stuck together.
Quentin

I get this question a lot. Washer is flooding the house, water everywhere, won't stop. The first thing I say is unplug the washer. If the water is still coming in,(which it will on a stuck valve) shut off the water faucets. If that is not possible shut the water meter off. If you can stop the washer with the timer then I would say instead of a bad valve you have a plugged water level pressure hose. Look at this diagram: As you can see the rubber tube from the bottom of the tub allows air pressure to push against the switch till it shuts down the valve and starts the wash cycle. Remedy this problem: Simply remove the tube from the switch and blow it out. Use them lungs!. Get that sand and trash out of the sump. Reconnect the hose tightly and pump out any standing water. Then restart the machine. If you have a good tight connection the machine should start working like normal. No parts needed! LOL!

DOES IT DO THIS ON EVERY WASH OR SOMETIMES? IF SOMETIMES, CHECK LID SWITCH( THERE'S A LITTLE HOLE WHEN YOU OPEN THE LID, ON THE LID SHOULD HAVE A LITTLE PLASTIC PIECE THAT GOES IN THAT HOLE. THE SWITCH IS UNDER, INSIDE THAT HOLE. YOU CAN GET A PEN OR KEY TO SEE IF IT'S BROKEN.)
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CHANGE THE LID SWITCH

That sounds like your lid switch. This switch is located on the top. Raise the lid, Looking down at the washing machine it is the little hole. If you push it down with your finger on mine it's grey in color. The problem is that the switch is not getting pushed down far enough. if you pull it down manually with your hand a little farther you should hear it click over and the machine might scare you as it starts up into the rinse cycle. You can purchase them pretty cheap online at any applince site.