We have examined a simple chemical reaction in a temperature gradient; 2F <==> F2. A mechanical model was used, based on Stillinger and Weber's 2- and 3-body potentials. Equilibrium and non-equilibrium molecular dynamics simulations showed that the chemical reaction is in local thermodynamic as well as in local chemical equilibrium (delta(r)G = 0) in the supercritical fluid, for temperature gradients up to 10(12) K m(-1). The reaction is thus diffusion-controlled. The velocity distributions of both components were everywhere close to being Maxwellian. The peak distributions were shifted slightly up or down from the average velocity of all particles. The shift depended on the magnitude of the temperature gradient. The results support the assumption that the entropy production of the reacting mixture can be written as a product sum of fluxes and forces. The temperature gradient promotes interdiffusion of components in the stationary state, a small reaction rate and an accumulation of the molecule in the cold region and the atom in the hot region.