  We prove Poisson upper bounds for the heat kernel of the Dirichlet-to-Neumann
operator with variable H{\"o}lder coefficients when the underlying domain is
bounded and has a C 1+$\kappa$-boundary for some $\kappa$ > 0. We also prove a
number of other results such as gradient estimates for heat kernels and Green
functions G of elliptic operators with possibly complex-valued coefficients. We
establish H{\"o}lder continuity of $\nabla$ x $\nabla$ y G up to the boundary.
These results are used to prove L p-estimates for commutators of
Dirichlet-to-Neumann operators on the boundary of C 1+$\kappa$-domains. Such
estimates are the keystone in our approach for the Poisson bounds.
