Context. It has been found from ISO, Spitzer, and Herschel observations that molecular hydrogen, H2, can form on warm grains. Numerical models of interstellar chemistry have failed to reproduce the observed formation rates of H2, which remains a difficulty when interpreting observations of photon-dominated regions (PDRs). Aims: We attempt to include as much experimental and theoretical information as possible to describe H2 formation in astrophysical environments to solve this problem. Methods: We modified our "Meudon PDR code" to include a detailed treatment of H2 formation mechanisms including: i) the Langmuir-Hinshelwood mechanism taking into account the contribution of the different sizes of dust grains in the diffusion processes; and ii) the Eley-Rideal mechanism. Results: We are able to form H2 even in regions where the dust temperature is higher than 25 K. We also show that formation by the Eley-Rideal mechanism can be a significant source of gas heating. We derive line intensities for various astrophysical conditions. Conclusions: Our approach results in a higher H2 formation rate than for the "standard" 3 × 10-17 nH n(H) cm3 s-1 expression.