  In this paper we explore the different mechanisms that affect the thermopower
of a band insulating perovskite (in this case, SrTiO$_3$) when subject to
strain (both compressive or tensile). We analyze the high temperature, entropy
dominated limit and the lower temperature, energy-transport regime. We observe
that the effect of strain in the high-temperature Seebeck coefficient is small
at the concentration levels of interest for thermoelectric applications.
However, the effective mass changes substantially with strain, which produces
an opposite effect to that of the degeneracy-breakups produced by strain. In
particular, we find that the thermopower can be enhanced by applying tensile
strain in the adequate regime. We conclude that the detrimental effect of
strain in thermopower due to band splitting is a minor effect that will not
hamper the optimization of the thermoelectric properties of oxides with
t$_{2g}$-active bands by applying strain.
