Hey Abril,
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Could be a bunch of different things, considering it was a sudden change I would also suggest looking at the main heating element, could be as simple as a burnt off wire or needing a new element entirely. You should also be able to check the thermometer (depending on which kind it is) If you can access the wires to the heating element and by the time you get there, its not obvious why its not working, you can also ohm out the element, once again should have some resistance, should be stable. Should not be an open circuit nor 0 ohms, elements are normally between 30-70 ohms, most in the lower range of that.
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If its electric, check for ohms between the 2 wires, should be a stable number, not fluctuating all over the place or if its mechanical, see if the contacts on thermostat are closing or opening at any time, should be able to put your volt meter on it and see if it ever does anything.
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And if it is mechanical, then you can also check for the little copper tube going into the tank one way or another, coming in contact with the water. Sometimes, they develop a crack or break for some mystical reason, this pretty much renders them useless as the gas or liquid pushing the contacts closed once it heats up and expands in the copper tube, has escaped and it is now, useless. Its called Capillary tube.
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I would definetley start there as well as checking safeties, could be it overworked itself. Most thermostats will have a little red button on it that you can push and then it will “click” which means it was in fact tripped, if you don’t feel or hear anything, then its still working okay.
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Let us know how it goes, coffee machine are always fun.