  Strong magnetic fields are observed in a substantial fraction of upper main
sequence stars and white dwarfs. Many such stars are observed to exhibit
photometric modulations as the magnetic poles rotate in and out of view, which
could be a consequence of magnetic perturbations to the star's thermal
structure. The magnetic pressure is typically larger than the gas pressure at
the star's photosphere, but much smaller than the gas pressure in the star's
interior, so the expected surface flux perturbations are not clear. We compute
magnetically perturbed stellar structures of young $3 \, M_\odot$ stars that
are in both hydrostatic and thermal equilibrium, and which contain both
poloidal and toroidal components of a dipolar magnetic field as expected for
stable fossil fields. This provides semi-analytical models of such fields in
baroclinic stably stratified regions. The star's internal pressure,
temperature, and flux perturbations can have a range of magnitudes, though we
argue the most likely configurations exhibit flux perturbations much smaller
than the ratio of surface magnetic pressure to surface gas pressure, but much
larger than the ratio of surface magnetic pressure to central gas pressure. The
magnetic pole is hotter than the equator in our models, but a cooler magnetic
pole is possible depending on the magnetic field configuration. The expected
flux variations for observed field strengths are $\delta L/L \! \lesssim \!
10^{-6}$, much smaller than those observed in magnetic stars, suggesting that
observed perturbations stem from changes to the emergent spectrum rather than
changes to the bolometric flux.
