Long-term observations indicate a substantial cooling in the mesosphere and lower thermosphere (MLT) over the last 3--4 decades. Available model studies have primarily considered the effects of CO2 doubling expected to occur in the future. We present a benchmark estimate of radiative forcing in the MLT due to the increase of CO2 mixing ratio from 313 ppm to about 360 ppm (or by 15%) observed over the last four decades. The Spectral Mesosphere/Lower Thermosphere Model is employed for retrocasting the atmospheric response. As expected, the thermal response is predominantly negative. As a function of altitude, the cooling maximizes in the mesosphere at about 3 K, practically vanishes at 100--120 km, and grows to 10--15 K in the thermosphere. Although this vertical shape is remarkably consistent with various sets of observations, the magnitude of the cooling rate is smaller by about a factor of 2--10. This suggests that other mechanisms, e.g., the ozone depletion, might have contributed substantially to the negative temperature trend.