Protein thermostability is important for fitness, but it is difficult to measure stability for every protein in the proteome. Fortunately, protein thermostability is correlated with prokaryotic species’ optimal growth temperature (OGT), which can be predicted from other genome features. The link between sequence features, OGT, and protein stability makes it possible to build models that predict protein stability from protein amino acid sequences. Such prediction models are particularly useful for eukaryotic species, which have large proteomes with limited annotation. Models that can predict temperature sensitivity across the prokaryote-eukaryote divide would help inform how eukaryotes adapt to elevated temperatures, such as those predicted by climate change models. In this study we test whether prediction models can cross the prokaryote-eukaryote divide to predict both prokaryotic and eukaryotic protein stability. We compare models built using a) the whole proteome, b) Pfam domains, and c) individual amino acid residues. Proteome-wide models accurately predict prokaryote optimal growth temperatures (r2 up to 0.93), while site-specific models demonstrate that nearly half of the proteome is associated with optimal growth temperature in both Archaea and Bacteria. Comparisons with the small number of eukaryotes with temperature sensitivity data suggest that site-specific models are the most transferable across the prokaryote-eukaryote divide. Using the site-specific models, we evaluated temperature sensitivity for 323,850 amino acid residues in 2,088 Pfam domain clusters in Archaea and Bacteria species separately. 190,063 residues (58.7%) are significantly associated with OGT in Archaea species and 244,256 residues (75.4%) are significantly associated with OGT in Bacteria species at a 5% false discovery rate. These models make it possible to understand which Pfam domains and amino acid residues are involved in temperature adaptation and facilitate future research questions about how species will fare in the face of increasing environmental temperatures.