I view gender as mostly a cultural construct, though in more mainstream literature (as well as certain legal contexts) it’s regarded as a social one.
The concept of gender is “newer” than its biological analogue (sex) in both science and, seemingly, pop discourse. As such, the collective understanding of the former is less-developed in Western society.
As a socio-cultural concept, then, gender is closer to character (a social concept) than to temperament (biological and psychological). By definition, the idea of sex becomes more relevant to one’s temperament than to character.