Gibbs random field (GRF) models work well for synthesizing complex natural-looking image data with a small number of parameters; however, estimation methods for these parameters have a lot of problems. This paper addresses the analysis problem in a new way by examining the role of the temperature parameter of the Gibbs distribution. Studies of the model energy with respect to the temperature are used to indicate pattern equilibrium and regions of different behavior, analogous to the existence of distinct phases in a physical system. The results on equilibrium and regions of different ``phases'' are offered as explanations for some of the peculiar behavior of current estimation algorithms.