Can I Use Type K thermocouple wires (extension) for an E type thermocouple? What aspects need to be considered for this different type of the thermocouple vs extension wire connection?

 You should always use thermocouple wire or thermocouple extension wire that matches the type of thermocouple that you are using (in your case E).  Thermocouple or thermocouple extension wire of the proper type must be used all the way from the sensor to measuring instrument.  Using a different type or copper wire will in most cases introduce significant errors in the readings.  Each junction that you introduce a different metal will create a thermocouple and a voltage that will add or subtract from your measurements.  The error will change based  on the temperature at that point and the metals that are (wire types) that are used. 

You can use terminal blocks of different materials without significant errors since the errors will be canceled out.

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