Derrive a transfer function or PDE from a simulation

Hello,

I would like to know if it is possible in MATLAB to make a simulation and derrive the PDE or transfer function from it, which describes the simulated system.

For example:

In my case I want to know the temperature transfer function of a plastic extruder, which melts plastics with different temperatures in different zones.

I would like to simulate this in an easy way by using a cylinder, which has 3 heat generators(G1...G3) and 3 temperature sensors(T1...T3) in MATLAB. My goal is to retrieve a equation, which describes the heat transfer through the barrel, so that I can retrieve the temperature in a function like F(G1,G2,G3) = .... = T1,T2,T3.

A rough but very common solution is for example: F(s) = (1/1+ST )* e^-st

By doing so I could use the the equation to make a control loop in SIMULINK and simulate a PID controller.