From the trip-lite manual
"Connect Battery Temperature Sensing Cable—OPTIONAL (not on 612 models)
The battery temperature sensing function prolongs battery life by adjusting the charge float voltage level based on battery temperature. Connect the sensor cable (the cable, included with select models, has an RJ style connector on one end and a black sensor on the other) to the RJ style jack located on the side of the Inverter/Charger labeled “Remote Temp. Sense.” With user-supplied electrical or duct tape, affix the sensor to the side of the battery below the electrolyte level. Make sure that nothing, not even tape, comes between the sensor and the side of the battery. To guard against false readings due to ambient temperature, place the sensor between batteries, if possible, or away from sources of extreme heat or cold. If the sensor cable is not used, the Inverter/Charger will charge according to its default 25º C values."
Most other temperature sensors attach to the ground lug. Your charging values are compensated by the battery temperature.
See attached chart from lifeline manual.
-greg