Let us consider heat conduction in a dilute plasma. The calculation of the diffusion coefficient is similar to the calculation of the electrical conductivity. The effective collision rate is given by

$ \omega \approx \frac{n q^4}{m^2 v^3} $

where $ n $ is the number density, $ q $ is the electric charge, $ m $ is the electron mass and $ v $ is the thermal velocity. The diffusion coefficient is given by

$ D \approx v^2/\omega \approx \frac{m^2 v^5}{n q^4} $

The heat flux is given by Fick's law

$ F_c \approx D \nabla \left(n k T \right ) \approx \frac{\left(k T \right )^{5/2}}{m^{1/2} q^4} \nabla \left(k T \right ) $

where $ T \, $ is the temperature and $ k $ is the Boltzmann constant.