Rising temperatures due to anthropogenic climate change pose a threat to wild Atlantic salmon populations in their natural habitat and to farmed populations during their major growth phase in coastal (seawater) net pens. While tremendous gains have been made in farmed salmon production through artificial selection programs, these have not considered the improvement of high-temperature tolerance. We therefore used two thermal challenge protocols to examine variation among families in a commercial salmon breeding program: a rapid temperature increase using loss of equilibrium as the endpoint (critical thermal maximum; CTmax) and a slower increase with mortality or morbidity as the endpoint (incremental thermal maximum; ITmax). High estimated heritability values were obtained for both (h² = 0.47 and 0.40, respectively), meaning that improved high-temperature tolerance should be attainable for farmed salmon through artificial selection. Furthermore, given that farmed salmon are not many generations removed from wild, this also suggested that wild populations may have some capacity to adapt to increasing temperatures brought about by climate change. However, we found no genetic or phenotypic correlations between CTmax and ITmax, and only weak (or no) genetic and phenotypic correlations between them and other traits predicted to influence thermal tolerance (body size and condition factor, ventricle size, and hematocrit).