Maybe you have seen instructions for modeling thermal processes in circuit simulators?
This is when current = power, voltage = temperature, capacity = heat capacity, etc ....
Something similar to the one shown in the figure, only in more detail and deployed.
Doing this is basically the same as using an analog computer to solve differential equations. You would need to convert your physical model to dimensionless form, and then map it onto an equivalent electrical circuit. You can do it, but it requires a bit of work. To succeed, you will need to have a good understanding of the physics involved, and how to create an appropriate model.
Indeed, a better description of SPICE is a nonlinear numerical integration engine; it's dimensioned for circuits (amps, volts, seconds..) but you can rename a voltage or current as any complementary unit in any other problem: velocity and acceleration in mechanics, temperature and power in thermal; etc.
So it's not an unusual practice to incorporate models in exactly this way. You occasionally see thermal models for transistors where there's an extra output pin corresponding to its power dissipation, which you connect to an RC circuit* which models temperatures of junction, case, heatsink and etc., as the case may be.
*Thermal problems obey the heat equation, which only has real poles or fractional power solutions in the resulting transfer functions**. We can approximate the latter as the former for some desired degree of accuracy.
**For linear materials, of course. Nonlinear materials could exhibit thermal shock waves... but I'm not aware of any system that exhibits such. It would have to have a negative tempco of thermal conductivity I think? Or maybe it's more mundane, like, chemical reaction fronts can move faster than heat transfer in the material, explosives for example; but nah, that's a nonlinearity of the material's heat capacity (you could model a kinetic reaction as a one-time discontinuity in heat capacity: that is, on heating the substance, its temperature starts accelerating then suddenly rises stepwise for zero additional external heat input), nothing to do with its heat transfer. Anyway, needless to say this is nothing you need to worry about in practice.
Tim
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