Following a similar logic as above, one can derive the kinetic model for thermal conductivity of a dilute gas:
Consider two parallel plates separated by a gas layer. Both plates have uniform temperatures, and are so massive compared to the gas layer that they can be treated as thermal reservoirs. The upper plate has a higher temperature than the lower plate. The molecules in the gas layer have a molecular kinetic energy  which increases uniformly with distance  above the lower plate. The non-equilibrium energy flow is superimposed on a Maxwell-Boltzmann equilibrium distribution of molecular motions.
Let  be the molecular kinetic energy of the gas at an imaginary horizontal surface inside the gas layer. The number of molecules arriving at an area  on one side of the gas layer, with speed  at angle  from the normal, in time interval  is 
These molecules made their last collision at a distance  above and below the gas layer, and each will contribute a molecular kinetic energy of
where  is the specific heat capacity. Again, plus sign applies to molecules from above, and minus sign below. Note that the temperature gradient  can be considered to be constant over a distance of mean free path.
Integrating over all appropriate velocities within the constraint 
yields the energy transfer per unit time per unit area (also known as heat flux):
Note that the energy transfer from above is in the  direction, and therefore the overall minus sign in the equation. The net heat flux across the imaginary surface is thus
Combining the above kinetic equation with Fourier's law
gives the equation for thermal conductivity, which is usually denoted  when it is a dilute gas:
Similarly to viscosity, Revised Enskog Theory yields an expression for thermal conductivity that reduces to the above expression in the limit of infinite dilution, and which can be written as 
where  is a term that tends to unity in the limit of infinite dilution, accounting for excluded volume, and  is a term accounting for the transfer of energy across a non-zero distance between particles during a collision.