Most traits are polygenic, and the contributing loci can be identified by genome-wide association studies. The genetic basis of adaptation (adaptive architecture) is, however, difficult to characterize. Here, we propose to study the adaptive architecture of traits by monitoring the evolution of their phenotypic variance during adaptation to a new environment in well-defined laboratory conditions. Extensive computer simulations show that the evolution of phenotypic variance in a replicated experimental evolution setting can distinguish between oligogenic and polygenic adaptive architectures. We compared gene expression variance in male Drosophila simulans before and after 100 generations of adaptation to a novel hot environment. The variance change in gene expression was indistinguishable for genes with and without a significant change in mean expression after 100 generations of evolution. We suggest that the majority of adaptive gene expression evolution can be explained by a polygenic architecture. We propose that tracking the evolution of phenotypic variance across generations can provide an approach to characterize the adaptive architecture.