splitting sensor signal line
It depends of your sensor.

Analog:


If it's an RTD, then no, because the circuit needs to drive a current through the RTD and measure the voltage across the resistor, if you have 2 circuit, current will add-up and the voltage won't match expectation.
If it's a voltage based sensor, like a thermocouple, it should be fine as long as there isn't some active compensation or active signal filtering.
If it's a current based sensor, then you would have to add some circuitry.


Digital:
If its a 2 wire communication digital sensor, then you can have an active master to read out the sensor and you can passively "tap" the wire to catch the readout.

You can provide more detail about your sensor (like a reference, datasheet).