The kinetics of escape of cesium atoms into an antirelaxation coating is experimentally studied in the temperature range 298-335 K in a cell with a lock when the working volume of the cell and a stem with the metal are subjected to individual thermostating. Under all experimental conditions, the kinetic curve is found to be well described by a two-exponential function with fast and slow components. This kinetics is shown not to obey the Arrhenius law for the temperature range of changing the working volume temperature at a constant temperature of the stem with the metal. During simultaneous but different changes in the working volume temperature and the temperature of the stem with the metal, the temperature dependences of the fast and slow components of the kinetics decomposes into segments where the Arrhenius law is obeyed. The separation point is likely to be the melting temperature of the coating material. At high temperatures, the activation energy of escape of cesium atoms into the coating is found to be higher than that at low temperatures by approximately an order of magnitude.