I would redo the measurements, it's an oddball thermistor 4k at 25°C and usually the beta is much higher.
3k, 4.7k and 5k at 25°C are available, and my math your beta is around 2900-3000 whereas 3100 is the lowest you usually see.
Sometime AC hum pickup or extra cable capacitance can give wrong readings. These thermistors are usually
Cantherm MF52 family or in glass MF58, from china or at Digi-Key.
Common is 10k at 25°C and beta 3950.
I have some old
Taylor Thermor transmitters, they die if you connect them to a bench power supply at 3V, the IC latches up unless you add 47R resistor to lower dV/dt.
Most of the
Taylors Thermors I had died, either they drifted off frequency when cold or IC shorted when I ran them on the bench.
So far LaCrosse temperature transmitters are absolute garbage, what a waste of money.
Oregon Scientific/Radio Shack is very good but hard to find in town.