The short answer is ‘no’.
It is important that the entire circuit must be the same calibration type. Even if you're using calibrated wire that has been tested in a calibration laboratory, they cannot and should not be substituted one for another. The Electro Motive Force (EMF) output of each thermocouple type is different and unique from all other types. You want to be sure that you've selected the right calibrated wire for the temperature range of your application.
For example placing a Type J with EMF thermoelectric power of about 30µV/°F into a control circuit programmed for Type K with thermoelectric power of about 22µV/°F (or vice versa) will cause significant errors in temperature reading.
This incorrect use of thermocouple wire can result in more energy use and ruined parts that must be scrapped.
If you're unsure of the thermocouple wire you should be using, especially in high temperature heat treatment applications, consult the ABC's of thermcouple or contact us for assistance.