I’m not sure I understand you here. Your use of the word heritable causes me to thing hereditary, but then you state not genetic. I don’t understand how that can coincide.
A perfectly reasonable question. Your confusion arises from the differences between "genetic" and "hereditary," the former being a subset of the latter. "Genetic" is determined by genes, the core of which is DNA. Yet it turns out that there are heritable traits that are not determined by DNA, that can be inherited in response to environmental factors. One can literally change the heritable traits of an animal by how it is treated. These traits are not passed via DNA in genes, but by messenger RNA found in mitochondria. These are not genetic, but epigenetic.
For example, wolves can double in size in but five generations depending upon how much food is available; feed them more and the next generation is born larger and the next generation be larger still even if the extra food is withdrawn (hence this is not a matter of prenatal nutrition). Similarly, cut the food and it takes generations for the average size to come down. This is not due to genetics or selection, but it is a heritable response to environmental conditions.
Another example, one can take a population of stickleback fish, observe them and pull all the dominant fish from the population. At that point, the environmental stressor of not having dominant fish allows otherwise less dominant fish an opportunistic move into that role, to become dominant fish. Pull those dominant fish and crossbreed them with recessive fish, and the fish that became dominant will pass on those traits, producing dominant progeny. The principle works even across the species barrier!
Dog and horse breeders focused upon temperament have known this intuitively for decades. We simply have a label for it now.