Background: Biologists studying adaptation under sexual selection have spent considerable effort assessing the relative importance of two groups of models, which hinge on the idea that females gain indirect benefits via mate discrimination. These are the good genes and genetic compatibility models. Quantitative genetic studies have advanced our understanding of these models by enabling assessment of whether the genetic architectures underlying focal phenotypes are congruent with either model. In this context, good genes models require underlying additive genetic variance, while compatibility models require non-additive variance. Currently, we know very little about how the expression of genotypes comprised of distinct parental haplotypes, or how levels and types of genetic variance underlying key phenotypes, change across environments. Such knowledge is important, however, because genotype-environment interactions can have major implications on the potential for evolutionary responses to selection. Results: We used a full diallel breeding design to screen for complex genotype-environment interactions, and genetic architectures underlying key morphological traits, across two thermal environments (the lab standard 27 degrees C, and the cooler 23 degrees C) in the Australian field cricket, Teleogryllus oceanicus. In males, complex three-way interactions between sire and dam parental haplotypes and the rearing environment accounted for up to 23 per cent of the scaled phenotypic variance in the traits we measured (body mass, pronotum width and testes mass), and each trait harboured significant additive genetic variance in the standard temperature (27 degrees C) only. In females, these three-way interactions were less important, with interactions between the paternal haplotype and rearing environment accounting for about ten per cent of the phenotypic variance (in body mass, pronotum width and ovary mass). Of the female traits measured, only ovary mass for crickets reared at the cooler temperature (23 degrees C), exhibited significant levels of additive genetic variance. Conclusions: Our results show that the genetics underlying phenotypic expression can be complex, context-dependent and different in each of the sexes. We discuss the implications of these results, particularly in terms of the evolutionary processes that hinge on good and compatible genes models.