One-minimum U-shaped temperature profiles of the dissociation constant (K(m)) have been observed experimentally with a variety of enzyme-substrate (E-S) systems. The increase of E-S affinity with falling temperature ("positive thermal modulation of affinity"), which opposes the cold-induced reduction in catalytic velocity, has been often interpreted as significant for both immediate and evolutionary temperature compensations and of major importance in setting thermal limits in ectothermic organisms. This role was denied to enzymes from endotherms, on the ground that their minimal K(m) values were situated well below their normal body temperature. Evidence is presented in this report that affinity changes described by U-shaped profiles can simply be the consequence of intrinsic kinetic properties of the E-S system. Theoretical modeling is achieved by combining the classical expression for the Michaelis constant with Transition State Theory expressions for the three rate constants involved. It provides for the U-shape of the K(m) vs. T profile and allows for the derivation of an equation for identifying its inversion point. Modeling of V(max) and V(min) (reaction velocity under conditions of substrate saturation and of dilution, K(m)>>[S], respectively) is also included. An expression was formulated for predicting the "critical temperature," T(C), corresponding to the low-temperature break in Arrhenius lines. Using existing K(m) data from literature, concerning a variety of E-S systems, our modeling proved to be highly satisfactory. Our own experiments show that glucose uptake by rat brain synaptosomes can be regarded as a special case of basically the same kinetic scheme, and that the U-shaped temperature modulation of apparent K(m) for glucose conversion is also in full agreement with our kinetic modeling. These experiments indicate that positive thermal modulation, although based on intrinsic kinetic properties of the underlying E-S system, may have an adaptive role in endotherms as well, linked, however, to their tolerance to hypothermia.