The kinetic temperatures in molecular clouds are usually considered to range upward from about 10 K (e.g., Dickman 1975). These temperatures are generally measured by observing the CO J = 1 → 0 transition and assuming that this line is optically thick and thermalized. This assumption also underlies estimates of the total mass and distribution of molecular material in our galaxy based on CO surveys. Because a significant amount of molecular material could in principle be missed by galactic CO surveys, a search was undertaken for “ultra-cold” molecular gas, by which is meant an excitation temperature, Tex < 5 K. No evidence was found for a large amount of such material (Evans, Rubin, and Zuckerman 1980), but many clouds with Tex between 5 and 10 K were found. To determine if this low Tex is due to low kinetic temperature, low density, or low CO abundance, we have undertaken observations of a large number of clouds in the J = 2 → 1 CO line and the J = 1 → 0 13CO and CO lines. These observations will be analyzed to determine the properties of these clouds.