The problem of the optimal control of aerosol emissions into the stratosphere to stabilize the Earth's climate is considered based on the zero-dimensional energy balance model. The global surface-temperature deviation from the undisturbed value is the state variable, and the albedo of the artificial aerosol layer, whose time variations are functionally related to the change in the total mass of aerosol particles and, consequently, the rate of their emissions, is the control variable. The problem is solved with and without consideration for the system phase path and control variable constraints for the given performance measure (objective function). Unlike previous studies, the aerosol emission scenarios are not set a priori, but represent a rigorous solution of the optimal control problem, ensuring the minimization of the objective function. The method is illustrated using the RCP8.5 scenario of growing concentration of greenhouse gases in the atmosphere. The approach considered in this paper can be easily extended to the cases of applying other known methods of climate engineering to manipulate the climate.