The blue thing is a temperature transmitter, which reads the RTD signal by sourcing a constant current through the RTD, reading the voltage drop, and outputing a linearized temperature signal whose range is defined on the label, which appears to be a scaled output of 0-10V (but it's hard to read.)
The 2-wire RTD connects to the input terminals shown as a rectangle/resistor. The label tells you that the transmitter needs a 24Vdc power supply to run the tranmitter. One terminal is labeled (+) so that's where the 24Vdc (+) connects. The zero V/common side of the 24V is not marked, so it's probably a 3-wire transmitter where the power supply (-)/common connects to the output signal terminal labeled (-).
I can read none of the micro's terminal labels, but look for 0-10Vdc analog input.