  In this article, we consider the problem of homogenising the linear heat
equation perturbed by a rapidly oscillating random potential. We consider the
situation where the space-time scaling of the potential's oscillations is
\textit{not} given by the diffusion scaling that leaves the heat equation
invariant. Instead, we treat the case where spatial oscillations are much
faster than temporal oscillations. Under suitable scaling of the amplitude of
the potential, we prove convergence to a deterministic heat equation with
constant potential, thus completing the results previously obtained in
\cite{MR2962093}.
