Is intellectual capacity a hereditary trait?

Yes: While many things affect one's intellectual abilities, heredity is a major contributor. However, one can improve on background inherited abilities by study, practice, increased exposure, utilizing good learning skills, etc. Other activities such as a healthy diet, adequate sleep and even exercise are also helpful in increasing and maintaining good intellectual function.

To a degree: There are no human behavioral traits that are simply hereditary or not (as, say, eye color pretty much is). The key concept is "heritability", a statistical measure of the influence of genes versus environment. The best estimates put iq at about 60% heritable--about mid-range for behavioral traits. This means that it can be significantly affected by childhood, education, illness, training, effort.