The temperature dependencies of the kinetic parameters K _M and k _cot ( = \fracV_max [E₀ ] )\left( { = \frac{{V_{max} }}{{[E_0 ]}}} \right) are often used in comparative physiology to identify mechanisms of thermal adaptation, e.g. in the case of the NADP⁺-dependent isocitrate dehydrogenase of Idus idus. This approach has merits, but entails a considerable risk of misinterpretation when the composite nature of the kinctic parameter is not taken into account. Since the thermal dependence of the elementary steps is known in principle, and since the dependence of complex reaction systems on temperature may be derived and compared with the observations, a survey of the most common reaction schemes for enzymatic reactions and the temperature dependencies of the associated kinetic parameters is given. Many, but not all, observations may, in the light of this theory, be given plausible mechanistic interpretations. However, care must be taken to ensure that the parameters are truly comparable, by use of data extrapolated to saturation of the enzyme with substrate. K _M is not necessarily equal to S_0.5 or a direct measure of the affinity of the active site for substrate.