This paper describes a mathematical/computational model of emotions and temperaments (or personalities). This model has been implemented on cognitive mobile robots. Emotions such as fear, anger, sadness, happiness, disgust, surprise, and others can be modeled, and can vary due to reinforcers (e.g. rewards and punishments). The model incorporates exponential decay of the reinforcement effects, so without continual reinforcers the emotion will return to their steady-state values. It is shown that emotions and temperament are coupled through the theory. Most models of emotions do not relate emotions to temperament. The constants used in the model of emotions are related to the temperament of the robot. The main five temperaments discussed include Extrovert/Introvert, Neurotic/Rational, Conscientious/Careless, Agreeable/Disagreeable, and Open/Reticent. The emotion and temperament model developed here has been incorporated into SS-RICS, which is a cognitive architecture developed at the Army Research Laboratory and tested in both mobile robots and in simulators.