Aims: Micrometeoroids (cosmic dust with size between a few μm and ~1 mm) dominate the annual extraterrestrial mass flux to the Earth. We investigate the range of physical processes occurring when micrometeoroids traverse the atmosphere. We compute the time (and altitude) dependent mass loss, energy balance, and dynamics to identify which processes determine their survival for a range of entry conditions. Methods: We develop a general numerical model for the micrometeoroid-atmosphere interaction. The equations of motion, energy, and mass balance are simultaneously solved for different entry conditions (e.g. initial radii, incident speeds and angles). Several different physical processes are taken into account in the equation of energy and in the mass balance, in order to understand their relative roles and evolution during the micrometeoroid-atmosphere interaction. In particular, to analyze the micrometeoroid thermal history we include in the energy balance: collisions with atmospheric particles, micrometeoroid radiation emission, evaporation, melting, sputtering and kinetic energy of the ablated mass. Results: Low entry velocities and grazing incidence angles favor micrometeoroid survival. Among those that survive, our model distinguishes (1) micrometeoroids who reach the melting temperature and for which melting is the most effective mass loss mechanism, and (2) micrometeoroids for which ablation due to evaporation causes most of the the mass loss. Melting is the most effective cooling mechanism. Sputtering-induced mass loss is negligible.