The interplay between the energy distribution function of adatoms and the rate of diatom formation in catalytic reaction is studied by means of mean field rate equations. The recombination of adatoms is described as a multi-channel process where adatom desorption arises from several energy levels. It is shown that the distribution function can be computed, analytically, as a function of the ratio between recombination probability and rate constant for energy disposal to the solid. This parameter is the key quantity of the kinetics since it governs both reaction rate and the shape of the energy distribution function. It is found that, in order to obtain steady state conditions, the control parameter is constrained within a well defined interval of values which result lower than unity. It is shown that a kinetic transition takes place for the highest value of the parameter, which entails hyperthermal reaction rate.