Heat equation with time dependent properties

Hi everyone

I'd need to solve a heat equation in a 2D domain (basically a rectangle with insulating lateral edges and two temperatures at the top and at bottom) and the rectangle is formed of three different materials overlayered.

I'm not an expert about how to solve a pde in Matlab but before getting into the details I'd like to know if it's possible proceed with the further request that I have. I'd like to know if operations changing the properties of the material can be performed over the time at each time step, e.g. I'd need to change the the heat conductivity (or other properties) at each time step and therefore I'd like that the pde solver starts with certain boundary and initial conditions, it performs the first time step, than I change some properties and the solver proceed with these new modified features and so on.

Is it possible? if yes do you have any example of it?

Thanks in advance and cheers MatteP