An air-conditioned room with automatic regulation of the climate systems serving it using complex control algorithms is one of the most difficult objects for calculating non-stationary thermal regime, so to date, this method is insufficiently studied. At the same time, such objects are typical when organizing the internal microclimate of civil buildings. In this paper, we consider the mathematical formulation and solution of the problem of changing the temperature of internal air in a room equipped with automated local cooling systems and a background supply ventilation system under variable thermal influences. The main equations connecting the most important components of the heat flow in the room are analyzed. The dependence on time for the deviation of the room air temperature from the setpoint is presented, and the expression for the moment of time at which the maximum temperature deviation is observed, with a jump-like change in the heat flow from heat sources in the case of regulating the equipment of local cooling systems according to the integral law. Calculations were performed to confirm the analytical solution obtained using a finite-difference approximation of the differential equations of heat balance and heat transfer on the example of one of the currently existing residential buildings in the climatic conditions of Moscow, taking into account the structural characteristics of the building and the thermal properties of its enclosing structures. It is noted that the greatest deviation of the temperature from the setpoint (dynamic control error) in the first approximation is inversely proportional to the cubic root of the transmission coefficient of the regulator, as well as the moment of time for which this deviation is observed. The obtained relations are proposed to be used for an analytical assessment of the non-stationary thermal regime of an air-conditioned room served by local cooling systems equipped with an automation system with an integral law of regulation, to check the conditions of human comfort and safety, as well as to determine the required parameters of the regulator.