  We present a space-time multiscale method for a parabolic model problem with
an underlying coefficient that may be highly oscillatory with respect to both
the spatial and the temporal variables. The method is based on the framework of
the Variational Multiscale Method in the context of a space-time formulation
and computes a coarse-scale representation of the differential operator that is
enriched by auxiliary space-time corrector functions. Once computed, the
coarse-scale representation allows us to efficiently obtain well-approximating
discrete solutions for multiple right-hand sides. We prove first-order
convergence independently of the oscillation scales in the coefficient and
illustrate how the space-time correctors decay exponentially in both space and
time, making it possible to localize the corresponding computations. This
localization allows us to define a practical and computationally efficient
method in terms of complexity and memory, for which we provide a posteriori
error estimates and present numerical examples.
