In this work, a novel method is proposed to establish the most suitable operational temperature for an enzyme reactor. The method was based on mathematical modelling of the thermal stability and activity of the enzyme and was developed using thermodynamic concepts and experimental data from free and immobilized inulinases (2,1-beta-D fructan frutanohydrolase, EC 3.2.1.7) from Kluyveromyces marxiantis, which were used as examples. The model was, therefore, designed to predict the enzyme activity with respect to the temperature and time course of the enzymatic process, as well as its half-life, in a broad temperature range. The knowledge and information provided by the model could be used to design the operational temperature conditions, leading to higher enzyme activities, while preserving acceptable stability levels, which represent the link between higher productivity and lower process costs. For the inulinase used in this study, the optimum temperature conditions leading to higher enzyme activities were shown to be 63 degrees C and 57.5 degrees C for the free and immobilized inulinases, respectively. However, according to the novel method of approach used here, the more appropriate operating temperatures would be 52 degrees C for free and 42 degrees C for immobilized inulinases, showing that the working temperature is not necessarily the same as the maximum reaction rate temperature, but preferably a lower temperature where the enzyme is much more stable. (c) 2006 Elsevier Ltd. All rights reserved.