If a thermocouple is pushed part way into the kiln wall, will the thermocouple read hotter or cooler than the firing chamber temperature?
During firing, the temperature in the firebricks or ceramic fiber wall is lower than the firing chamber temperature. If the firing chamber is 2000 degrees F, the outer firebrick surface may be only several hundred degrees. The closer you go toward the outside of the firebrick, the lower the temperature.
So if the thermocouple is pushed into the firebrick wall, the thermocouple will register a lower temperature than the firing chamber. This will cause the controller to keep the elements turned on longer to compensate for the low reading, resulting in an overfire.
If the thermocouple extends into the firing chamber by 1/8" instead of the recommended 3/4" - 1", the overfire will be only a few degrees. If you are firing slowly and the heat has soaked into the firebricks, there might not be an overfire at all. But if the thermocouple tip has been pushed well past the firebrick surface, the overfire could be as high as several hundred degrees F.
Another factor is distance to the elements. If the thermocouple hole is near an element, the kiln might not overfire at all when the thermocouple tip is flush with the firebrick surface.
It is very important not to disturb the thermocouple, either by bumping it with a shelf or twisting it. Twisting the thermocouple can cause the two thermocouple wires to touch each other at some point inside the kiln wall. This could short out the thermocouple tip and cause the thermocouple to read the temperature from inside the firebrick wall where the thermocouple wires are touching. This would overfire the kiln.