What a great question! Like the others have said, it is a non-linear relationship and a direct, universal conversion is not possible.
A digital thermometer is essentially a voltmeter that reads the very small voltage produced along the thermocouple wires (in the 4 mV range, probably). Based on the non-linear thermocouple calibration curves (i.e. K, T, J, etc), the thermometer converts that millivolt reading into a temperature DIFFERENCE between the hot end (the probe) and the cold end (the termination at the thermometer).
So, to know the actual temperature at the probe, you need to know both the temperature difference (millivolts converted to degrees per calibration curve) and the ambient temperature at the so-called cold joint at the thermometer. It is the variation in ambient temperature that will defeat attempts to make a universal conversion table between K and T.
But, for a cold joint temperature of around 69F, the following values should give you at least an approximation. I developed these very quickly by feeding a T signal from my calibrator into a thermometer that was expecting K - kind of like what you are planning. The CJ temp varied between 68.5F and 69.2F as I was making the readings.
- Table:
temp at temp
hot joint indication
of T t/c on K thermometer
190.0 195.9
195.0 201.4
200.0 207.0
205.0 212.7
210.0 218.3
As the ambient temperature at the thermometer moves away from 69F, these approximate values will have increasing error.
Jim