My father showed me how much faster hot water freezes in an experiment we did when I was a kid. How many of us owe our fathers for what seems to be innate curiosity now that we are adults :)
I fall on the side of nurture with regard to curiosity. _Everybody_ has "the curiosity trait", but in some environments it's discouraged: "Stop asking so many questions.", or "I don't know and why do you care?", or simply giving wrong answers.