The paper presents the first laboratory measurement of the rate constant for quenching the CO₂ (01¹0) state during collisions of CO₂ molecules with O atoms at temperatures realized near the Earth's mesopause. The measurement was carried out with a hollow-cathode glow discharge in the temperature range 206-358 K. The measured values are significantly smaller than those commonly used in solving the non-LTE CO₂ problem for the vibrational states of the mode V₂ in the atmospheres of the Earth, Venus, and Mars. The measured temperature dependence of the rate constant is approximated by a simple relation, which is recommended for solving the above problem. The use of the new rate-constant values significantly decreased the rate of cooling by the CO₂ 15-μm emission in the terrestrial lower thermosphere as compared to the previous estimates obtained for this rate. Over the most area of the Earth's surface, the maximum cooling rate occurs at an altitude of about 110 km and amounts to about 20 K/day.