A mathematical model for simultaneously studying the effect of substrate concentration and temperature on beta-cyclodextrin (beta-CD) production by cyclodextrin glycosyltransferase (CGTase) was developed. The kinetic parameters, involved in a Michaelis-Menten model and thermal stability of CGTase, were determined. The kinetic parameters show that raising the temperature not only increased the reaction rate of the enzyme but also its affinity for the substrate. However, an increase in the temperature reduced the thermal stability of the enzyme. Therefore, the developed model that expresses both the reaction rate and the stability of the enzyme was used to determine the optimum temperature that provided a high reaction rate with good stability. The importance of developing the model is to demonstrate its successful application to practically determine the optimum condition that represents a compromise between a process with a high productivity and one with a high working efficiency. (C) 2011 Elsevier Ltd. All rights reserved.