Express reverse diode voltage drop as a function of temperature
Germanium diodes are not obsolete, they are better than silicon ones and have better temperature stability and parameters. The function that you are looking for is a datasheet parameter. You can easily measure it, its a function of current or voltage change based on temperature. Its called a diode temperature characteristic.

The characteristic will change in quadrants 1 and 3 based on the temperature, meaning the voltage and current through the diode will change with the temperature in a border.



The characteristic and the original image.

Formulas and explanations.