Nauman,

Well, you could construct a simple 1D thermal model (Fourier's law) and then build a simple realtionship between the heat transported, and the power applied to the TEC, and deduce the temperatures in your system.

There's nothing special about a model that can simulate cooling to -40degC.

You need to understand the equations that govern the TEC, and have a model for the way in which you eject the heat from the system (convected radiatior? Conduction to a large heatsink mass? Radiative transport? etc.)

Look at this doc it may be helpful for your topic. Good luck.

You can refer to this research article. They used compact modelling method to model a thermoelectric.

Article Analytical and numerical parameter extraction for compact mo...