At room temp does it show room temp + 250f?
Or does it show room temp plus a smaller amount?
I would say the issue you are having is that you have the wrong setting in your PID controller for the Type of TC you have hooked up to it.
at 698 F (370 C) a type J TC will read 20.745 millivolts while a type K will read 7.65 millivolts. That is a huge difference.
Keep in my that the MV above is not exact as we aren't factoring the junction temperature but its close enough.
I would verify the setting in the PID controller first and go from there.