Genetic architecture of adaptation is traditionally studied in the context of local adaptation, viz. spatially varying conditions experienced by the species. However, anthropogenic changes in the natural environment pose a new context to this issue, that is, adaptation to an environment that is new for the species. In this study, we used crossbreeding to analyze genetic architecture of adaptation to conditions not currently experienced by the species but with high probability of encounter in the near future due to global climate change. We performed targeted interpopulation crossing using genotypes from two core and two peripheral Triticum dicoccoides populations and raised the parents and three generations of hybrids in a greenhouse under simulated desert conditions to analyze the genetic architecture of adaptation to these conditions and an effect of gene flow from plants having different origin. The hybrid (F1) fitness did not differ from that of the parents in crosses where both plants originated from the species core, but in crosses involving one parent from the species core and another one from the species periphery the fitness of F1 was consistently higher than that of the periphery-originated parent. Plant fitness in the next two generations (F2 and F3) did not differ from the F1, suggesting that effects of epistatic interactions between recombining and segregating alleles of genes contributing to fitness were minor or absent. The observed low importance of epistatic gene interactions in allopolyploid T. dicoccoides and low probability of hybrid breakdown appear to be the result of permanent fixation of heterozygosity and lack of intergenomic recombination in this species. At the same time, predominant but not complete selfing combined with an advantage of bivalent pairing of homologous chromosomes appears to maintain high genetic variability in T. dicoccoides, greatly enhancing its adaptive ability.