A longstanding idea in evolutionary physiology is that an enzyme cannot jointly optimize performance at both high and low temperatures due to a trade-off between stability and activity. Although a stability-activity trade-off has been observed for well-characterized examples, such a trade-off is not imposed by any physical chemical constraint. To better understand the pervasiveness of this trade-off, I investigated the stability-activity relationship for comparative biochemical studies of purified orthologous enzymes identified by a literature search. The nature of this relationship varied greatly among studies. Notably, studies of enzymes with low mean synonymous nucleotide sequence divergence were less likely to exhibit the predicted negative correlation between stability and activity. Similarly, a survey of directed evolution investigations of the stability-activity relationship indicated that these traits are often uncoupled among nearly identical yet phenotypically divergent enzymes. This suggests that the presumptive trade-off often reported for investigations of enzymes with high mean sequence divergence may in some cases instead be a consequence of the degeneration over time of enzyme function in unselected environments, rather than a direct effect of thermal adaptation. The results caution against the general assertion of a stability-activity trade-off during enzyme adaptation.