  We construct a spectral sequence converging to the homology of the ordered
configuration spaces of a product of parallelizable manifolds. To identify the
second page of this spectral sequence, we introduce a version of the
Boardman--Vogt tensor product for linear operadic modules, a purely algebraic
operation. Using the rational formality of the little cubes operads, we show
that our spectral sequence collapses in characteristic zero.
