NTC : And more calibration

Let's really calibrate our NTC, for reference it is sold as a  3950 NTC, 100k at 25 °C

The formula is still

 Beta= TxTref x ln (Rref/R) / (T-Tref)

with Tref: Reference temperature, normally 25°C
        Ref : Resistance value at Tref

Which can be transformed to

ln(Ref/R)=B*(T-Tref)/(T*TRef)
or
ln(Ref)=B*(T-TRef)/(T*TRef)+ln(R)

The left part is a constant, so if we have 2 values, T1/R1 and T2/R2, they 'll have the same ln(Ref)

The two equal parts are

B*(T1-TRef)/(T1*Tref)+ln(R1)=B*(T2-TRef)/(T2*Tref)+ln(R2)

that can be expressed as

B=ln(R1/R2)*(T1*T2)/(T2-T1)

NB: All temperature are in Kelvin in the formulas, so you have to add 273.15

We just need two points to compute beta. Let's put the whole thing in the fridge to have both ambient and ~ 5 degrees.

We end up with our two points : T=21°C, R=112k and T=5°, R=217K, convert to kelvin, put that in your favorite spreadsheet to get

=> B=-3382

Now we have beta, we can compute Ref

ln(Ref)=B*(T-TRef)/(T*TRef)+ln(R)
We can compute the right part for our 2 points, and get Ref=96 K

It is significantly different from the given value of Beta=-3950, Ref=100k
The real ones are Beta=-3382, Ref=96k

A note of warning, the above is as accurate as your temperature measurements are.
I only have a kitchen thermometer, so i don't expect more than 1° accuracy.