Climate change is expected to affect biological systems across multiple scales through its direct effects on the physiology of individual organisms. Therefore, to predict how communities and ecosystems will be impacted by changes in climate, it is key to understand the extent to which ectotherm physiology can change through thermal adaptation. In this thesis, we examine the influence of possible constraints on thermal adaptation, as predicted by the Metabolic Theory of Ecology. In Chapter 2 we describe the consequences of violating a key assumption of a model used for quantifying the thermal performance curve, i.e., the relationship of biological rates with temperature. We then proceed in Chapter 3 to evaluate the impact of thermodynamic constraints on the evolution of the thermal performance curves of phytoplankton. We show that thermodynamic constraints have a very weak effect on thermal adaptation, with phylogenetically structured variation being present across the entire thermal performance curve. Further support for such a conclusion is obtained in Chapter 4 through a phylogenetic comparative analysis of the evolution of thermal sensitivity across prokaryotes, phytoplankton, and plants. This reveals that thermal sensitivity is much more variable than expected, as it can change drastically within short amounts of evolutionary time. In Chapter 5, we finally investigate thermal adaptation at the molecular level, examining if changes in temperature can alter the effects of nonsynonymous mutations. We show that across prokaryotes, mutations become increasingly detrimental to the stability of proteins with temperature. In response, thermophile species evolve enzymes that are more robust to mutations and exhibit low substitution rates. Overall, these results further our understanding of how thermal physiology evolves and indicate areas where the theory – as it currently stands – may need to be modified.