100129-1325 EST
Jakewhis:
Suppose this is a thermocouple sensor. Disconnect the sensor cable from the display instrument. Connect a meter, such as a Fluke 27, to the sensor leads. A J type (iron-constantan) produces about 55 microvolts/C relative to the ambient temperature of your meter lead terminations to the thermocouple leads. If you get a steady reading and the temperature of the sensor is constant, then it may not be a sensor problem. But does not exclude noise added to the signal when the sensor is connected to the the monitor.
Continuing with the same type of sensor connect a short at the monitor input and the input voltage is therefore 0. This is equivalent to the sensor and the instrument being at the same temperature. Thus, the instrument should read close to room temperature assuming there is a zero reference in the monitor. Reading should be stable.
If a thermistor sensor, then after disconnecting from monitor use your ohmmeter to measure resistance. Should be stable. If so put a fixed resistor of about the resistance of the sensor at the input of the monitor and see if the reading is stable.
Same for an RTD, but may be a lower resistance.
A Dallas 1-wire sensor would be much more difficult for you to evaluate.
http://en.wikipedia.org/wiki/Thermocouple
has typical voltage constants.
.