  We prove the following gradient inequality for the subelliptic heat kernel on
nilpotent Lie groups $G$ of H-type:
  $$|\nabla P_t f| \le K P_t(|\nabla f|)$$ where $P_t$ is the heat semigroup
corresponding to the sublaplacian on $G$, $\nabla$ is the subelliptic gradient,
and $K$ is a constant. This extends a result of H.-Q. Li for the Heisenberg
group. The proof is based on pointwise heat kernel estimates, and follows an
approach used by Bakry, Baudoin, Bonnefont, and Chafa\"i.
