I want to model the transfer function of a resistor mathematically, and am after some resources / tips on if it's possible to do so.
For example, if I put 1V into a 1 Ohm resistor, I want to know how long and how (shape) it will take to reach a steady state temperature, given 25 deg C ambient.
I.e.
$$ \frac{T(s)}{V(s)} = ??? $$
Where T(s) is the laplace transform of temperature T(t), measured in say Kelvin.
I understand there are a lot of factors which will affect this model (material, size, shape, ambient (?)), but I'm not sure where to even start. A datasheet shows the heat rise at a certain load, but not really how it gets there. I can't find a time-domain function for the temperature rise either.