We propose a method to compute the transmission through correlated heterostructures by combining density functional and many-body dynamical mean field theories. The heart of this combination consists in porting the many-body self-energy from an all electron basis into a pseudopotential localized atomic basis set. Using this combination we study the effects of local electronic interactions and finite temperatures on the transmission across the Cu 4 CoCu 4 metallic heterostructure. It is shown that as the electronic correlations are taken into account via a local but dynamic self-energy, the total transmission at the Fermi level gets reduced (predominantly in the minority-spin channel), whereby the spin polarization of the transmission increases. The latter is due to a more significant d-electron contribution, as compared to the noncorrelated case in which the transport is dominated by s and p electrons.