We discuss the possibilities of use of the new generation of desktops for solution of one of the most important problems of weather forecasting: real-time prediction of thunderstorms, hails and rain storms. The phenomena are associated with development of intensive convection and are considered as the most dangerous weather conditions. The most perspective way of the phenomena forecast is computer modeling. Small dimensional models (1 - D and 1.5 - D) are the only available to be effectively use in local weather centers and airports for real-time forecasting. We have developed one of such models: 1.5 - D convective cloud model with the detailed description of microphysical processes and have investigated the possibilities of its parallelization on multi-core processors with the different number of cores. The results of the investigations have shown that speed up of cloud evolution calculation can reached the value of 3 if 4 parallelization threads are used.