In a genetic epidemiology study of a trait, prior to collecting genotype data the foremost task is to test for familial aggregation and examine heritability. Recently, functional traits have drawn attentions from investigators. Here, to test for familial aggregation of a functional trait in the family studies, a test constructed based on the leading functional principal component of heritability, which is a summary measure of temporal genetic variation in a functional trait, is proposed. The p-value of the test can be approximated by a permutation procedure given the family structure. The asymptotic distribution of the test statistic is derived. Simulations are carried out to examine the size and the power of the test. The proposed methods are applied to the total cholesterol data in the Framingham Heart Study.