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Background Molecular markers and knowledge of traits associated with heat tolerance are likely to provide breeders with a more efficient means of selecting wheat varieties able to maintain grain size after heat waves during early grain filling. Results A population of 144 doubled haploids derived from a cross between the Australian wheat varieties Drysdale and Waagan was mapped using the wheat Illumina iSelect 9,000 feature single nucleotide polymorphism marker array and used to detect quantitative trait loci for heat tolerance of final single grain weight and related traits. Plants were subjected to a 3 d heat treatment (37 °C/27 °C day/night) in a growth chamber at 10 d after anthesis and trait responses calculated by comparison to untreated control plants. A locus for single grain weight stability was detected on the short arm of chromosome 3B in both winter- and autumn-sown experiments, determining up to 2.5 mg difference in heat-induced single grain weight loss. In one of the experiments, a locus with a weaker effect on grain weight stability was detected on chromosome 6B. Among the traits measured, the rate of flag leaf chlorophyll loss over the course of the heat treatment and reduction in shoot weight due to heat were indicators of loci with significant grain weight tolerance effects, with alleles for grain weight stability also conferring stability of chlorophyll (‘stay-green’) and shoot weight. Chlorophyll loss during the treatment, requiring only two non-destructive readings to be taken, directly before and after a heat event, may prove convenient for identifying heat tolerant germplasm. These results were consistent with grain filling being limited by assimilate supply from the heat-damaged photosynthetic apparatus, or alternatively, accelerated maturation in the grains that was correlated with leaf senescence responses merely due to common genetic control of senescence responses in the two organs. There was no evidence for a role of mobilized stem reserves (water soluble carbohydrates) in determining grain weight responses. Conclusions Molecular markers for the 3B or 6B loci, or the facile measurement of chlorophyll loss over the heat treatment, could be used to assist identification of heat tolerant genotypes for breeding. Electronic supplementary material The online version of this article (doi:10.1186/s12870-016-0784-6) contains supplementary material, which is available to authorized users.