Type J Thermocouple Signal Conditioning to 0-5V
Unless you have the "cold-junction" offset handled by some other method which you did not mention in your question, it is not recommended to use a simple op-amp to "condition" a thermocouple signal.  

Analog Devices makes a range of specialty "Thermocouple Interface Amplifiers". Highly recommended to use one of those.  There are some "break-out boards" which feature the complete thermocouple conditioning ready to use.

Ref: https://en.wikipedia.org/wiki/Thermocouple#Requirement_for_a_reference_junction

Ref: http://www.analog.com/en/products/amplifiers/specialty-amplifiers/thermocouple-interface-amplifiers.html#thermocouple-interface-amplifiers

Example: https://www.sparkfun.com/products/13266

Example: https://www.adafruit.com/products/269