Change size of part during thermal analysis to mimic 3D-printing

Hello,

I'm trying to find a way to give an estimate of how much heat there will be in a component during a 3d-printing operation.

My idea was to have a part, which I cut using a plane and solidification, then move the plane in order to let the part "grow" for each printed layer. During this there is heat/energy load on the surface for each layer.

Ideally I would like to have the simulation to not add a new layer (move the plane) and add heat until the average temperature of the part is below a certain value. The goal is to find a time for cooling between each printed layer.

I've tried using a plane + solidify where the plane's translation is bound to a parameter that increments on each regeneration (by using relation) but sadly this did not work. My question is: Is it even possible t change the geometry during a thermal simulation and would it be possible to constrain the heat load for each layer by measuring the temperature of the parts current state?