Prokaryotes evolved to thrive in an extremely diverse set of habitats, and their proteomes bear signatures of environmental conditions. Although correlations between amino acid usage and environmental temperature are well-documented, understanding of the mechanisms of thermal adaptation remains incomplete. Here, we couple the energetic costs of protein folding and protein homeostasis to build a microscopic model explaining both the overall amino acid composition and its temperature trends. Low biosynthesis costs lead to low diversity of physical interactions between amino acid residues, which in turn makes proteins less stable and drives up chaperone activity to maintain appropriate levels of folded, functional proteins. Assuming that the cost of chaperone activity is proportional to the fraction of unfolded client proteins, we simulated thermal adaptation of model proteins subject to minimization of the total cost of amino acid synthesis and chaperone activity. For the first time, we predicted both the proteome-average amino acid abundances and their temperature trends simultaneously, and found strong correlations between model predictions and 402 genomes of bacteria and archaea. The energetic constraint on protein evolution is more apparent in highly expressed proteins, selected by codon adaptation index. We found that in bacteria, highly expressed proteins are similar in composition to thermophilic ones, whereas in archaea no correlation between predicted expression level and thermostability was observed. At the same time, thermal adaptations of highly expressed proteins in bacteria and archaea are nearly identical, suggesting that universal energetic constraints prevail over the phylogenetic differences between these domains of life.