  In this paper we characterize hemirings in which all $h$-ideals or all fuzzy
$h$-ideals are idempotent. It is proved, among other results, that every
$h$-ideal of a hemiring $R$ is idempotent if and only if the lattice of fuzzy
$h$-ideals of $R$ is distributive under the sum and $h$-intrinsic product of
fuzzy $h$-ideals or, equivalently, if and only if each fuzzy $h$-ideal of $R$
is intersection of those prime fuzzy $h$-ideals of $R$ which contain it. We
also define two types of prime fuzzy $h$-ideals of $R$ and prove that, a
non-constant $h$-ideal of $R$ is prime in the second sense if and only if each
of its proper level set is a prime $h$-ideal of $R$.
