Super critical heat transfer usin LBM

I am trying to validate the following paper on Super critical heat transfer as part of Master’s project.

Házi, Gábor, and Attila Márkus. “Modeling heat transfer in supercritical fluid using the lattice Boltzmann method.” Physical Review E 77.2 (2008): 026305.

But i am getting some problems while modelling the temperature distribution functions.If anyone has done it earlier or has any idea about it,please help me out.