The increase in enzyme-catalyzed reaction rates with temperature is typically modeled using Arrhenius or Eyring relations. Interpretation of extracted parameters is subject to multiple caveats. Here we analyze the impact of expected small temperature variations of underlying activation/Eyring parameters on this modeling. Linear Arrhenius/Eyring behavior can still be observed when the underlying activation energy or enthalpy and entropy vary with temperature. Modest variations - of the order of an H-bond energy over 60 °C - lead to large fractional deviations of and values derived from linear fits from their underlying values and to deviations of Arrhenius prefactors by orders of magnitude. In a family of related enzymes with similar activation free energies , small differences in temperature variation of and will lead to apparent enthalpy-entropy compensation and may scramble enzyme ordering based on or . For enzymes from cold and warm-adapted species having largely similar active sites, small temperature variations of and may explain large differences in apparent values. Similar considerations apply to interpretation of van 't Hoff plots of equilibrium measurements and related observations of enthalpy-entropy compensation. Complementary methods including simulations and multi-temperature static and time-resolved atomic-resolution structural studies should play a key role in interpreting temperature-dependent kinetic and equilibrium data from enzymatic systems.