"Multiplexing" thermocouples to an IO board
I've recently done some PCB design with thermocouples, and have learned about how finicky they can be if they aren't treated exactly as they're supposed to be.  If you want a precision of 0.5 degrees, you must be able to measure 20uV of precision across the leads of the thermocouple!  Do you really trust whatever multiplexing solution you use to introduce less than 20uV of noise?  Not to mention that you can no longer perform proper cold junction compensation.

I know that usual precise thermocouple equipment is very expensive, but you can spend a lot less than 20k euros and still measure each thermocouple individually.  I have used the MAX31855 in the past, which works very well.  It has a precision of 0.25 degrees, cold junction compensation, simple SPI interface, and it costs less than 5 euros per IC.  For the sake of accuracy and simplicity, I suggest you spend less than $200 on 40 of these thermocouple IC's instead of multiplexing the thermocouples.