Question-and-Answer Resource for the Building Energy Modeling Community
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The community of modelers I work with typically will take the 3D problem and do their best at turning it into a combination of 2D problems and use THERM. One reason is the error introduce by reducing the 3D into a series of 2D problems is far smaller than what you typically get when you are taking either and converting to a 1D problem.
I think you should think about this as a 3D-2D version of the ASHRAE Zone method or ISO 6946 where you calculate and upper and lower limit based on assumption of 1D heat flow (upper limit) and isothermal planes (lower limit). You could do the same assuming for 3-D assuming the 2D sections do not interact (upper limit) or interact completely in one plane (lower limit).
Unfortunately I cannot point you to an example.
For software, others mentioned comsol multiphysics, MATLAB, and heat3 in the comments, none of which is free. Instead of using MATLAB, one could do any similar programming in Python or GNU-Octave for free. As a free replacement of heat3 or comsol, you could look to elmer, an open source multiphysics, FEM software http://www.csc.fi/english/pages/elmer
I have not used elmer since I have been a comsol user for a number of years, but I wanted to suggest something that might be used as a comsol alternative.
You might also check to see if anyone has developed libraries for 3-D bridging in the Modelica buildings library. Again I'm not a user (yet) but I know that it is gaining a lot of attention. http://simulationresearch.lbl.gov/modelica
