Solutions of generalized Poisson's equation on a 3D surface

I have been solving the potential in a thin resistive film with electrodes on the surface of a cylinder by unwrapping it to a flat 2D problem and solving the generalized Poisson’s equation with a finite difference algorithm. I would like to consider more general curved surfaces, starting with the same topology of a cylinder, but stretched into things like a cone transition and such. I have tried to understand, whether FreeFEM can be used to solve on a general 3D surface that is tube like. Furthermore, the problem would then be made to be a multi-physics problem with the joule heating power dissipating into the substrate supporting the film, first steady state solutions, but late a full time varying heat equation solutions. Can anyone tell me if the 3D surface mesh solution is possible in FreeFEM and if so, then possible give me example or a direction to take to start?

You can find more informations about the 3d surface mesh here
and find some examples in the directory examples/3dSurf of the distrib.