Traditionally, the dependence of enzyme activity on temperature has been described by a model consisting of two processes: the catalytic reaction defined by Delta G(cat)(double dagger), and irreversible inactivation defined by Delta G(inact)(double dagger). However, such a model does not account in for the observed temperature-dependent behaviour of enzymes, and a new model has been developed and validated. This model (the Equilibrium Model) describes a new mechanism by which enzymes lose activity at high temperatures, by including an inactive form of the enzyme (E-inact) that is in reversible equilibrium with the active form (E-act); it is the inactive form that undergoes irreversible thermal inactivation to the thermally denatured state. This equilibrium is described by an equilibrium constant whose temperature-dependence is characterized in terms of the enthalpy of the equilibrium, Delta H-eq, and a new thermal parameter, T-eq, which is the temperature at which the concentrations of E-act and E-inact are equal; T-eq may therefore be regarded as the thermal equivalent of K-m. Characterization of an enzyme with respect to its temperature-dependent behaviour must therefore include a determination of these intrinsic properties. The Equilibrium Model has major implications for enzymology, biotechnology and understanding the evolution of enzymes. The present study presents a new direct data-fitting method based on fitting progress curves directly to the Equilibrium Model, and assesses the robustness of this procedure and the effect of assay data on the accurate determination of T-eq and its associated parameters. It also describes simpler experimental methods for their determination than have been previously available, including those required for the application of the Equilibrium Model to non-ideal enzyme reactions.