As there is no heater tape what shuts off the heat ,and how to test?

Bench test. With heater tore apart, energized, a volt meter connected across the sensor will indicate a voltage when it opens. take note of aproximate temperature and compare with the sensor temp rated value.
It takes a bit of skill to trouble shoot, repair, and put it back together. Toss it out if in doubt.

My Mighty Heater 1500 will run for 15sec then shuts off then repeats it over an over

I am not sure about the heater type, but likely the heater element controller shorted out or the heater elements shorted - hence the black around where the wires go into the electric box. If you're lucky, the wires shorted to the side of the box. With the power off, open up the electrical box, mark which wires go where, remove them from the board, remove the wires from the electric box, then using electrical tape, tape up the exposed ends of the wires. Spread them out so they do not touch each other. Turn on the 60 amp breaker - if it trips, then your wires are bad and need replaced. If it does not trip, then the problem is with the heater. Do not let anyone near the wires when testing them! Don't forget to turn off the breaker if it does not trip. Again, turn off the breaker if it did not trip.

the older units have the limit mounted on the heat exchanger straight in front as u look at unit. try taping on unit . newer units are on a circuit board . just for the heck of it unhook the green t-stat wire on termal bloc on unit. if the blower stops then replace t-stat.

My Patton PUH682 utility heater from 2011 is otherwise in excellent condition but Auto Safety Shut-Off seems to be a design problem. My overheat sensor quickly shut off the unit when surrounding air was cool. It is inside the bottom of the fan box wired between the on/off potentiometer and heating coils.
I identified it by turning on the heater and watched the metal contacts separate as it tripped. On my unit, the defective overheat sensor is hardwired. Since it was otherwise useless as a heater, I decided to jerry-rig it and hope for the best. I pried back the sheet metal edge of the fan box and wrapped the sensor with electrical tape. Then I took a very small squeezable metal paper clip and lined it with electrical tape. I clamped it over the overheat sensor and it fits perfectly to prevent the metal plates from separating. Now the heater works the way it should. The cable, coils and plug don't overheat on Hot setting and it runs continuously.

I have a presto heater what i did was tape the buzzer botton up. if the heater fall over the buzzer will not go off because it is taped shut. the problem is your buzzer is sticken. the heater works fine once you shut the botton shut. to eliminate the buzzer.

Under the main black knob is a bi-metal switch which shuts down the heat at various temps depending on your setting. Their is no timer.

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unplug remove the back check the heater box fuse and heating element,they are to your right,the fuse is on the left side top,and the heating element is the bottom half of the heater box,remove 2 screws,if you don't have a meter,you can tape the 2 fuse wires together to see if you get,heat,but you can;t leave it like that,it is only for a test,the heating element remove it and look for a broken wire-mike

Two possibilities. 1 failed upper or lower Tstat 2 Shorted element
To test element: disconnect both wires to element terminals. use continuity tester to see if there is continuity through element (one probe on each element terminal) If no continuity element is bad. Then test for continuity between each element terminal and the water heater itself.( one probe on element terminal and one probe grounded on bare metal or inner tank.) If there is continuity from terminal to ground, element is bad and also can cause tank to continue heating even when thermostat shuts off. This is because the thermostat only shuts off one pole of the 220 and a shorted element can continue heating from the 2nd pole.
If both elements test OK and water heater heats the full tank( tank feels hot at bottom element access panel when no hot water for 2 hours) most likely the lower thermostat is bad.

remove the lower acess panel and there is a tech sheet / troubleshooting guide taped to te back side of it,, in there is detailed explaination of all your issues you may encounter with your machine.
I usually set to a test/diag mode and check to make sure your heater is working, after that if heater check ok youd want to listen for proper water amount being pump around interior of d/w(usually you can hear not really pumping with much force).
try pushing the sani-rinse. heated dry, sani-rinse, heated dry.. all lights should lite, indicating your in hte diag mode, it will then cycle through the tests afeter about 45 secs or so the motor will engage immedialty open the door assy and feel the heater coil for heat,if cold cancel test with the cancel button and try again.( i like to confirm the heater cycle twice),if you coil is still cold refer to the heat cycle test strip for repair.
aferer exiting hte test the clean light willnolonger be blinking regardles of repairing issue or not. perhaps it was a fluke happening youll be alble to run you unit, should it happen again immedialty youllnknow you a problem yoll need to adress