  Thermal X-ray emission from rotation-powered pulsars is believed to originate
from localized "hotspots" on the stellar surface occurring where large-scale
currents from the magnetosphere return to heat the atmosphere. Lightcurve
modeling has primarily been limited to simple models, such as circular
antipodal emitting regions with constant temperature. We calculate more
realistic temperature distributions within the polar caps, taking advantage of
recent advances in magnetospheric theory, and we consider their effect on the
predicted lightcurves. The emitting regions are non-circular even for a pure
dipole magnetic field, and the inclusion of an aligned magnetic quadrupole
moment introduces a north-south asymmetry. As the aligned quadrupole moment is
increased, one hotspot grows in size before becoming a thin ring surrounding
the star. For the pure dipole case, moving to the more realistic model changes
the lightcurves by $5-10\%$ for millisecond pulsars, helping to quantify the
systematic uncertainty present in current dipolar models. Including the
quadrupole gives considerable freedom in generating more complex lightcurves.
We explore whether these simple dipole+quadrupole models can account for the
qualitative features of the lightcurve of PSR J0437$-$4715.
