Distribution of species across the Earth shows strong latitudinal and altitudinal gradients with the number of species decreasing with declining temperatures. While these patterns have been recognized for well over a century, the mechanisms generating and maintaining them have remained elusive. Here, we propose a mechanistic explanation for temperature-dependent rates of molecular evolution that can influence speciation rates and global biodiversity gradients. Our hypothesis is based on the effects of temperature and temperature-adaptation on stability of proteins and other catalytic biomolecules. First, due to the nature of physical forces between biomolecules and water, stability of biomolecules is maximal around + 20°C and decreases as temperature either decreases or increases. Second, organisms that have adapted to cold temperatures have evolved especially flexible (but unstable) proteins to facilitate catalytic reactions in cold, where molecular movements slow down. Both these effects should result in mutations being on average more detrimental at cold temperatures (i.e. lower mutational robustness in cold). At high temperatures, destabilizing water–biomolecule interactions, and the need to maintain structures that withstand heat denaturation, should decrease mutational robustness similarly. Decreased mutational robustness at extreme temperatures will slow down molecular evolution, as a larger fraction of new mutations will be removed by selection. Lower mutational robustness may also select for reduced mutation rates, further slowing down the rate of molecular evolution. As speciation requires the evolution of epistatic incompatibilities that prevent gene flow among incipient species, slow rate of molecular evolution at extreme temperatures will directly slow down the rate at which new species arise. The proposed mechanism can thus explain why molecular evolution is faster at warm temperatures, contributing to higher speciation rate and elevated species richness in environments characterized by stable and warm temperatures.