  Auscher, McIntosh and Tchamitchian studied the heat kernels of second order
elliptic operators in divergence form with complex bounded measurable
coefficients on $\mathbb{R}^n$. In particular, in the case when $n=2$ they
obtained Gaussian upper bound estimates for the heat kernel without imposing
further assumption on the coefficients. We study the fundamental solutions of
the systems of second order parabolic equations in the divergence form with
bounded, measurable, time-independent coefficients, and extend their results to
the systems of parabolic equations.
