Climate warming is threatening biodiversity by increasing temperatures beyond the optima of many ectotherms. Owing to the inherent non-linear relationship between temperature and the rate of cellular processes, such shifts towards hot temperature are predicted to impose stronger selection compared with corresponding shifts towards cold temperature. This suggests that when adaptation to warming occurs, it should be relatively rapid and predictable. Here we tested this hypothesis from the level of single-nucleotide polymorphisms to life-history traits in the beetle Callosobruchus maculatus. We conducted an evolve-and-resequence experiment on three genetic backgrounds of the beetle reared at hot or cold temperature. Indeed, we find that phenotypic evolution was faster and more repeatable at hot temperature. However, at the genomic level, adaptation to heat was less repeatable when compared across genetic backgrounds. As a result, genomic predictions of phenotypic adaptation in populations exposed to hot temperature were accurate within, but not between, backgrounds. These results seem best explained by genetic redundancy and an increased importance of epistasis during adaptation to heat, and imply that the same mechanisms that exert strong selection and increase repeatability of phenotypic evolution at hot temperature reduce repeatability at the genomic level. Thus, predictions of adaptation in key phenotypes from genomic data may become increasingly difficult as climates warm.