  We construct Green's functions for second order parabolic operators of the
form $Pu=\partial_t u-{\rm div}({\bf A} \nabla u+ \boldsymbol{b}u)+
\boldsymbol{c} \cdot \nabla u+du$ in $(-\infty, \infty) \times \Omega$, where
$\Omega$ is an open connected set in $\mathbb{R}^n$. It is not necessary that
$\Omega$ to be bounded and $\Omega = \mathbb{R}^n$ is not excluded. We assume
that the leading coefficients $\bf A$ are bounded and measurable and the lower
order coefficients $\boldsymbol{b}$, $\boldsymbol{c}$, and $d$ belong to
critical mixed norm Lebesgue spaces and satisfy the conditions $d-{\rm div}
\boldsymbol{b} \ge 0$ and ${\rm div}(\boldsymbol{b}-\boldsymbol{c}) \ge 0$. We
show that the Green's function has the Gaussian bound in the entire $(-\infty,
\infty) \times \Omega$.
