In annual plant species, flowering time is a major adaptive trait that synchronizes the initiation of reproduction with favorable environmental conditions. Here, we aimed at studying the evolution of flowering time in three experimental populations of bread wheat, grown in contrasting environments (Northern to Southern France) for 12 generations. By comparing the distribution of phenotypic and presumably neutral variation, we first showed that flowering time responded to selection during the 12 generations of the experiment. To get insight into the genetic architecture of that trait, we then tested whether the distribution of genetic polymorphisms at six candidate genes, presumably involved in the trait expression, departed from neutral expectation. To that end, we focused on the temporal variation during the course of the experiment, and on the spatial differentiation at the end of the experiment, using previously published methods adapted to our experimental design. Only those genes that were strongly associated with flowering time variation were detected as responding to selection. For genes that had low-to-moderate phenotypic effects, or when there was interaction across different genes, we did not find evidence of selection using methods based on the distribution of temporal or spatial variation. In such cases, it might be more informative to consider multilocus and multiallelic combinations across genes, which could be the targets of selection.