The paper considers second-order, strongly elliptic, operators H with complex almost-periodic
coefficients in divergence form on Rd. First,
it is proved that the corresponding heat kernel is Hölder
continuous and Gaussian bounds are derived with the correct small and large time asymptotic behaviour
on the kernel and its Hölder derivatives. Secondly, it is established that the kernel has a variety of
properties of almost-periodicity. Thirdly, it is demonstrated that the kernel of the homogenization Ĥ of
H is the leading term in the asymptotic expansion of t [map ] Kt.