Approximate the different situations using the heat eqn.

That said, what scale are you considering? Is this purely for academic purposes? In this data-driven era of IoT, vast amounts of data can be collected for thousands of scenarios, enabling the development of a predictive model—arguably a more practical approach.

If this is a long-term research project, focus on data collection first. Gather sufficient data for the geographical location (temperature, wind patterns, etc.), housing characteristics (wall materials, window types, etc.), and homeowners' habits (such as door-opening frequency and heating usage). The more parameters, the better. Once you have a robust dataset, you can build an ML model, making this an exciting and valuable research endeavour.

If this is a long-term project, build it up in stages of complexity while at the same time deploying the work to the web, as your goal is to eventually get the work out there. I have deployed machine learning models using a framework like Django, after creating the model using Python but not in that field. You need AWS (and Docker). The software components are reusable by just changing the underlying model and a bit of tweaking.

If a lumped parameter approach would be accurate enough for your purposes, you might express the room temperature as the result of a convolution between the ambient temperature and an impulse response describing (macroscopically) the propagation of heat along the walls. This is typically carried out in the Fourier domain by means of the transfer function.