We used temperature data from the Sounding of the Atmosphere with Broadband Emission Radiometry (SABER) on the the NASA TIMED satellite to quantify the connection between temperatures in the stratosphere and in the mesosphere and lower thermosphere. Specifically, we studied three winter periods where stratospheric temperatures were dynamically disturbed: February 2002, August, 2002, and February 2003. The SABER temperatures show a clear signature of mesospheric coolings in concert with stratospheric warmings. Mesospheric temperatures between 0.7 hPa and 0.01 hPa show a significant anticorrelation with stratospheric temperatures. For pressures <0.01 hPa, this anticorrelation breaks down, in disagreement with recent model results from a thermosphere-ionosphere-mesosphere general circulation model that suggest mesospheric coolings persist up to 110 km. Also, the lack of a clear correlation between stratospheric temperatures and those at 83--90 km suggests that measurements of the OH Meinel band temperatures at those altitudes may not be representative of the entire mesosphere.