You can definitely implement the simpler, 2D finite difference, heat equation (as shown in your video) in GH, I don’t think you need Ladybug for that.
However, the geometry you’re showing looks like it’s quite a bit more complicated then that. Specifically, your geometry will require modeling convective and radiative exchange between boundaries, involving the calculation of view factors and fluid exchange, respectively. Are you eventually going to model these components as well? It’s not as easy to calculate, and I think at that point it’d be easier to go to a specialized FEM tool, which is not available in Ladybug/Honeybee.
FYI, Ladybug tools does a lot more then just simulate solar radiation :), including building energy and thermal load simulation. It even supports 2D conduction heat transfer analysis (via the finite element method), through THERM, but it’s meant for envelope products, and doesn’t support the addition of a heat source.