Ohm's Law only applies to ideal resistors. It doesn't apply at all to non-linear elements like transistors and diodes, and can have significant errors when applied to real-world resistors.
Ohm's Law is an approximation...a model... of real behavior. And George Box said it best: "All models are wrong, some are useful."
A generalised picture of the resistor network (As I have understood it) is shown above. V1-V2 is the applied potential difference between the two faces (seems to be 20 V in your picture). V3, V4, V5, V6 etc are the node voltages you have already solved for.
To find the equivalent resistance, you need to divide the applied potential difference by the current ...
This is from some of the folks who make Kanthal wire.
It goes into some detail about designing things with Kanthal heating wires and elements.
At no point does it tell you how to calculate temperature from voltage and current or voltage and current from temperature because you can't do that.
You have to have the ambient temperature.
You have to have values ...