The classic approach to the description of the temperature-dependence of enzyme activity lumps both reversible and irreversible inactivations into one step. This generates an erroneous dependence of the enzymatic rate on temperature and the duration of assay. A two-step 'equilibrium model' has been proposed recently to correct these weaknesses. However. this model too has some drawbacks. At short assay times, there are two peaks on the rate-temperature-time surface. This difficulty with fast assays is avoided by slow assays; however, the latter carry a greater risk of irreversible denaturation. This problem disappears on increasing the order of the irreversible step from one to two, suggesting that a second-order equilibrium model may be appropriate for some thermal inactivations.