  We use dynamical mean-field theory to study how electronic transport in
multi-orbital metals is influenced by correlated (nominally) empty orbitals
that are in proximity to the Fermi level. Specifically, we study 2 + 1 orbital
and 3 + 2 orbital (i.e. t2g + eg ) models on a Bethe lattice with a crystal
field that is set so that the higher lying orbitals are nearly empty at low
temperatures but get a non-negligible occupancy at elevated temperature. The
high temperature regime is characterized by thermal activation of carriers
leading to higher magnetic response (i.e., thermally induced low-spin to
high-spin transition) and substantial influence on resistivity, where one can
distinguish two counteracting effects: increased scattering due to formation of
high spin and increased scattering phase space on one hand, and additional
parallel conduction channel on the other. The former effect is stronger and one
may identify cases where resistivity increases by a factor of three at high
temperatures even though the occupancy of the unoccupied band remains small (<
10%). We discuss implications of our findings for transport properties of
correlated materials.
