The relationship between low-level cloud optical depth and atmospheric and surface air temperature is examined in the control climate of thirteen climate models to determine if cloud optical depth-temperature relationships found in observations are replicated in climate models, and if climate model behavior found in control climate simulations provides information about the optical depth feedback in climate warming simulations forced by increasing carbon dioxide. A positive relationship between cloud optical depth and cloud temperature exists in all models for low clouds with relatively cold temperatures at middle and high latitudes, whereas a negative relationship exists for warmer low clouds in the tropics and subtropics. This relationship is qualitatively similar to that in an earlier analysis of satellite observations, although modeled regression slopes tend to be too positive and their inter-model spread is large. In the models, the cold cloud response comes from increases in cloud water content with increasing temperature, while the warm cloud response comes from decreases in physical thickness with increasing cloud temperature. The inter-model and inter-regional spread of low-cloud optical depth feedback in climate warming simulations is well predicted by the corresponding spread in the relationships between optical depth and temperature for the current climate, suggesting that this aspect of cloud feedback may be constrained by observations. Because models have a positive bias relative to observations in the optical depth-temperature relationship, shortwave cloud feedbacks for climate changes may be more positive than climate models currently simulate.