Yes intelligence has to do with heritability, there was initially an animal with had cognition (a word I much prefer instead of intelligence) this animal actually had descendants some of which are humans, we initially inherited this intelligence from him but also from other ancestors that developed this cognition latter as well.

You provided that we do not have a physiological model for intelligence, and I believe we will not have one for some decades at least if I'm to be optimist. That's a real large problem, another one is to relate this to genetics and environmental development, these would be a hard problem as far as I was told by some friends that are biologists.