Can you describe in more detail the problem you are trying to solve? The reason I am asking is that the textbook by Carslaw and Jaeger [1] has a chapter that appears, on the surface, to be what you are looking for topic-wise.
[1] H. S. Carslaw, J. C. Jaeger; Conduction of Heat in Solids, 2nd Ed.; Oxford University Press; 1959; pp. pp. 176-187, Chapter VI - The Flow of Heat in a Rectangular Parallelepiped.