This is an Arduino library for MOD-TC-MK2 rev.B with host board ESP8266-EVB rev.A

Tested with Arduino 1.8.0.
In order to work you have to install ESP8266 package: http://arduino.esp8266.com/versions/2.3.0/package_esp8266com_index.json
Once installed, select board: Olimex MOD-WIFI-ESP8266(-DEV).
Uploading the sketch and monitoring data are done via RX and TX line on the UEXT. So you need additional device to connect the computer to the host board (for example USB-serial cable). In the "Main Menu --> Tools --> Port" select the COM port of your device.
To upload the sketch host board must be in bootloader mode. To do so power the board while holding the button.
Once you have completed uploading the sketch connect the I2C lines between the host and the MOD-TC-MK2. If you are using UEXT cable but you need UEXT on the host for both MOD-TC-MK2 and the serial device (to monitor data) then you may need an UEXT splitter. Otherwise you can simply use jumper cables.

After all this is done you can open the "Serial Monitor" and watch the output values:
Example output:
External temperature: 22.25
Internal temperature: 22.9375
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External temperature: 22.25
Internal temperature: 22.9375
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If there is no thermocouple connected to the MOD-TC-MK2 an error message will be displayed:
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FAULT: Open Circuit
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YYYY/MM/DD
2017/02/01

Stanimir Petev, Olimex