Thermocouple amplifier and cold junction compensation
I already designed a simple amplifier for the thermocouple using
  LM358.


Unfortunately, the LM358 makes a very poor amplifier for thermocouples given that it has an input offset voltage that may be as high as +/- 3mV. Given that a thermocouple (K-type for example) produces 41 μV per degree celcius, it means that your temperature accuracy is only to within +/- 3000/41 = +/-73 degrees celcius.

Here is your proposed design and some figures from the LM358 data sheet and, at the bottom the graphs for various thermocouples: -



This is not the intelligent way to design thermocouple amplifiers - use a precision InAmp (like the AD8221) if you want anything like decent accuracy. Use a negative rail so that if someone connects the thermocouple backwards you can still retrieve measurements (albeit them being negative). The cold junction compensation is trivial so, get your basic amplifier design right first.