Phenotypic variance is attributed to genetic and non-genetic factors, and only the former are presumed to be inherited and thus suitable for the action of selection. Although increasing amounts of data suggest that non-genetic variability may be inherited, we have limited empirical data in animals. Here, we performed an artificial selection experiment using Drosophila melanogaster inbred lines. We quantified the response to selection for a decrease in chill coma recovery time and an increase in starvation resistance. We observed a weak response to selection in the inbred and outbred lines, with variability across lines. At the end of the selection process, differential expression was detected for some genes associated with epigenetics, the piRNA pathway and canalization functions. As the selection process can disturb the canalization process and increase the phenotypic variance of developmental traits, we also investigated possible effects of the selection process on the number of scutellar bristles, fluctuating asymmetry levels and fitness estimates. These results suggest that, contrary to what was shown in plants, selection of non-genetic variability is not straightforward in Drosophila and appears to be strongly genotype dependent.