I think the easiest way would be ANSYS workbench. You can select the analysis system from the toolbox that will lead you at every stage from creation of geometry, mesh generation to calculations and presenting results. If I remember correct you can chose between steady state and transient thermal analysis.
This seems like a simple geometry to model. You can do it in either, APDL or Workbench.
Having said that, more important to consider is the fact that if you are not very fluent in APDL, then the codes need a bit more time to understand, and application of load is a bit more tough. The meshing in this case will be mostly simple, as I presume that you are using simple square/rectangle geometry. But if your solid is of a complex shape- or you have holes in the body- you shall have much more trouble with the meshing (and would have to go for structured mesh, with concatenation in most cases).
Having said that, if you understand the codes well, then it coding shall be no problem at all. The next factor that comes into play will be, how many iterations do you want to make of the same, and with how many values that differ from each other. It shall be much easier to change the values (try and parametrize the values in the code, if you plan to use APDL.) of flux/shape/thickness etc in APDL if you plan to use the bodies for many successive iterations, and can lead the work to be much faster than in Workbench.
So, I guess, the answer to which software to use should depend completely on your proficiency levels with both, and the number of times you plan to repeat the simulations.