A numerical model is presented that allows an adequate description of the evolution of a liquiddroplet convective cloud developing under extreme conditions in the presence of high-power thermal sources on the land surface or in the atmosphere. The features of the life cycle and stages of clouds are studied on the basis of this model in relation to the distribution of environmental humidity and the time of action of a thermal source and its temperature and radius. It is shown that, owing to the action of an instantaneous energy source (an explosion), a convection flow develops in the form of a thermal, whereas a convection flow in the form of a jet develops above a long-acting energy source (fire). The features of the evolution and formation of precipitation in the clouds formed under the development of both convection forms are studied in detail.