Oven thermostat temp is off

Contact the maker. It sounds like the new thermostat is faulty.

https://www.google.com/search?q=Elmira+Northstar+1956B+inconsistent+temp

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The thermostat is mechanical using pressure from a waxstat style sender and is not adjustable.
I expect you are measuring with your probe in a different place to the sender unit; hence the differences.

If you have a "mechanical" thermostat you would need a new one. Of course, if the end of the thermostat (inside the oven) is broken, that will prevent the thermostat from "feeling the heat". (Same solution). Most ovens now in use electronic controls, with a thermistor inside the oven cavity. That would be the first part to check

There is a calibration method to adjust the oven thermostat plus/minus 35 degrees if it is a digital display. The method varies depending on the model range. This calibration method is used to adjust the thermostat if it is not keeping proper tempature. For example if you are setting the oven to 350 and the actual temp it is keeping is 325 then you could use the calibration method to adjust it plus 25 degrees to correct the temp. Just so you know electric ovens will keep a pretty even temp but gas ovens will vary by 40 or more degrees to keep an "average" temp. For example the burner will come on when the oven is 330 degrees and turn off at 370. 330+370 then divide by 2=350. So a oven thermometer may not show you the temp you set it at in a gas oven but does not mean the oven temp is off.

The temp indicator light goes on and off according to the temp selected.
The sensor referred to is part and parcel of the the thermostat, or temp selector
the fact the light goes on and off, shows that the thermostatt is working, but neccesserily at the correct temp.I maintain that the thermostat that controls the temp is faulty, and needs to be replaced.

Something is probobly wrong with the thermostat, it gets hot to warm up, but should lessen as it reaches your desired temp. If the thermostat is bad it will just keep going.

Normally you should have an appliance spare parts supplier in your area. They generally stock all range of spares for all appliances. You need to pull plug out of the wall and remove the panel covering the wiring to gain access to the oven thermostat. Look carefully on the body of the thermostat and record any numbers you see on a sticker that's present. Then remove knob off in front of thermostat and see if there is a nut attached to the centre which holds the thermostat in position or if there are 2 screws holding the thermostat in place. Use this information to order the thermostat also quoting the oven model number.

How much is it off? Adjustable with the thermostat knob. If too far for the knob setting then the thermostat is bad.
Eric

Yes you do need a new thermostat, just make sure that the sensor is not obstructed by anything. first.
Plz rate my solution
Thanks.

probably the element. to save wasting money, check continuity with a multimeter