The variational principle of irreversible entropy production as formulated by Rosenbluth, Hazeltine and Hinton is used to evaluate the electron thermal diffusion coefficient. Starting from an equal-temperature plasma kinetic equation using the drift approximation and assuming that a small periodic electrostatic non-uniformity exists within the plasma we derive an expression for the electron heat flux. In this derivation the full Fokker-Planck collision operator is employed and the effect of both like and unlike particles is included. The coefficient of electron thermal diffusion deduced from the electron heat flux expression is identical with the one deduced by Pogutse (up to a multiplicative factor), and is in qualitative agreement with the pseudoclassical result.