Wheat productivity is severely reduced by high temperatures. Breeding heat tolerant cultivars could be achieved by identifying genes controlling variation and using these to select superior genotypes. Here, we report the positional cloning of qYDH.3BL, a quantitative trait locus (QTL) on bread wheat chromosome 3B associated with yield stability under hot conditions. The QTL was constitutively expressed in deep soil, with the positive allele associated with an increase in grain yield, thousand grain weight, early vigour and plant biomass under elevated temperatures. We fine mapped the QTL interval to a region containing twelve predicted genes. Of those, one gene showed contrasted gene expression and sequence polymorphism among parental lines and near-isogenic lines. This gene is homologous to Seven In Absentia (SINA) genes, a family encoding E3 ubiquitin ligase proteins involved in the ubiquitin pathway for the degradation of target proteins. Near isogenic lines carrying the positive allele at qYDH.3BL under-expressed TaSINA at an early developmental stage and had increased biomass, grain number and size following heat stress. A sequence variation in the promoter region of TaSINA would explain contrasted gene expression. A survey of worldwide distribution indicates the positive allele haplotype became widespread from the 1950s through the CIMMYT wheat breeding programme but was, to date, selected for only in Mexico and Australia.