Thermoplastic parts obtained by selective laser melting of a powder bed (SLM process) have porosities which significantly reduce their mechanical resistance. These porosities are due to trapped air between polymer grains while polymer melts and grains coalesce. To understand the physical mechanism involved in the powder densification, the anisothermal coalescence of a powder bed has been simulated after the passage of the laser beam. Firstly we show that coalescence of spheres leads to roughly the same coalescence time as cylinders. It allowed us performing a 2D simulation using a C-NEM method implemented in Matlab® to assess the importance of the different physical phenomena involved in the process: polymer powder grain coalescence, interface welding, process temperatures, powder laser energy absorption. Two polymers were considered in the simulations: a PEEK and a PEKK. Surface tension and viscosity of studied polymers, which pilot coalescence phenomenon, were measured versus temperature. The geometry of powder bed was determined by Xray tomography. Laser absorption of thermoplastic powders were identified though a specific device and a calorimeter. The simulation was validated by comparing the simulation of flows for of known simple geometries: cylinder coalescence and pendant drop. The simulation was calibrated by adjusting thermal exchange coefficients thanks to measured melted depth. We have determined thermal and time orders of magnitude of the process. We mainly show that the temperature of the polymer may rise by several hundred degrees and decreases in a few tenths of a second, while densification process can take several tens of seconds. We have processing window for semicrystalline polymers. Then we could conclude that only amorphous thermoplastic powder with a very low molecular weight can be processed by SLM process.