The problem is really not so much of programming, but first of all a problem of classical theoretical physics (and, strictly speaking, the problem will be classical only if you consider non-condensed media) and mathematics, and not the simplest one. You really should go all the way by yourself. Also, don't try to find complete solution on the Web. In part of physics, there is a lot of literature with will also give you sufficient mathematical background, but you need to be confident in related fields of mathematics, which is not really a rocket surgery but might require good university-level education, maybe not on the level "real" mathematicians learn, but at the level of good physicists. When you build a model and find out how to translate the results in the thermal conductivity values (which is the most difficult part, I think) you can get to programming, which is much easier but not absolutely trivial. Don't hope for the help for "regular" software developers — my experience (and not only my) shows that they are not usually able to understand the problem. Besides, almost all modern software engineers have no idea of numeric calculations.

Instead, learn programming yourself, and seek the help from software developers on pure technological aspects of computing.

So, the only thing which would help is this:

http://lmgtfy.com/?q=Monte+Carlo+simulation+of+the+effective+thermal+conductivity[^].

Amazingly, top item is search results looks fully relevant: http://www.sciencedirect.com/science/article/pii/S0924013604005825[^].

I just wonder why we have to explain such things. After all, is OP a physicist or not?

--SA