A lumped-parameter mathematical model of an automotive magnetorheological (MR) fluid fan clutch was developed. This model is able to describe the average fluid temperature, average clutch temperature, and output fan speed as a function of time, input current, and fluid composition. The model also reproduces numerous features of fan operation observed experimentally and revealed a mechanism for some observed cases of hysteresis. However, it fails to capture certain other features which lead us to conclude that phenomena which are not included in the model, e.g., sedimentation and re-suspension, are important to the clutch behavior. In addition, the results indicate that certain physical properties need to be measured over a larger temperature range in order for the model to better predict the clutch behavior.