For what it's worth.........
Every wire connection from your temperature probe will introduce a voltage drop at that connection point.
Granted, we are down in the milli-volt range, but so is the output of the probe.
These voltage drops will introduce a signal to the PID that is less than the actual value being outputted from the probe.
An example would be if you wired the probe leads to a terminal block and then from the terminal block to the PID.
So, from the probe you would have a crimp connector (point #1) on the wire that is then connected to the terminal block (point #2), then on the other side of the terminal block (point#3) is another crimp connector (point #4) with the wire going to the PID having a crimp connector (point #5) and screwed to the PID unit (point#6)
Because there are two wires on the probe you then have 12 different connection points, each adding their own voltage drop to the total BEFORE it gets to the PID.
There are male/female fittings made for thermocouples to reduce these errors, such as those you can "plug" the probe into the PID box.
But, wiring the probe directly to the PID would certainly minimize these (12) connection point voltage drops and give better accuracy.
Hope that made sense.