The dissipation of the tidal energy deposited on eccentric planets may induce a heating of the planet that affects its atmospheric thermal structure. Here we study the influence of tidal heating on the atmospheric composition of the eccentric (e = 0.16) "hot Neptune" GJ 436b, for which inconclusive chemical abundances are retrieved from multiwavelength photometric observations carried out during primary transit and secondary eclipse. We build up a one-dimensional model of GJ 436b's atmosphere in the vertical direction and compute the pressure-temperature and molecular abundances profiles for various plausible internal temperatures of the planet (up to 560 K) and metallicities (from solar to 100 times solar), using a radiative-convective model and a chemical model which includes thermochemical kinetics, vertical mixing, and photochemistry. We find that the CO/CH4 abundance ratio increases with metallicity and tidal heating, and ranges from 1/20 to 1000 within the ranges of metallicity and internal temperature explored. Water vapour locks most of the oxygen and reaches a very high abundance, whatever the metallicity and internal temperature of the planet. The CO2/H2O abundance ratio increases dramatically with metallicity, and takes values between 1e-5-1e-4 with solar elemental abundances and 0.1 for a metallicity 100 times solar. None of the atmospheric models based on solid physical and chemical grounds provide a fully satisfactory agreement with available observational data, although the comparison of calculated spectra and observations seem to point to models with a high metallicity and efficient tidal heating, in which high CO/CH4 abundance ratios and warm temperatures in the dayside atmosphere are favoured.< Réduire