  Spider pulsars are binary systems containing an energetic millisecond pulsar
that intensely irradiates a closely orbiting low-mass companion. Modelling
their companion's optical light curves is essential to the study of the orbital
properties of the binary, including the determination of the pulsar mass,
characterising the pulsar wind and the star itself. We aim to generalise the
traditional direct heating model of irradiation, whereby energy deposited by
the pulsar wind into the stellar envelope is locally re-emitted, by introducing
heat redistribution via diffusion and convection within the outer stellar
envelope. We approximate the irradiated stellar envelope as a two-dimensional
shell. This allows us to propose an effective equation of energy conservation
that can be solved at a reduced computational cost. We then implement this
model in the \texttt{Icarus} software and use evidence sampling to determine
the most likely convection and diffusion laws for the light curve of the
redback companion of PSR J2215+5135. Redistribution effects concentrate near
the terminator line of pulsar irradiation, and can create apparent hot and cold
spots. Among the models tested for PSR J2215+5135, we find that all models with
heat redistribution are more likely than symmetric direct heating. The
best-fitting redistribution model involves diffusion together with a uniformly
rotating envelope. However, we caution that all models still present serious
systematic effects, and that prior knowledge from pulsar timing, spectroscopy
and distance are key to determine with certainty the most accurate
redistribution law. We propose an extension of the direct heating framework
that allows for exploring a variety of heat redistribution effects. Future work
is necessary to determine the relevant laws from first principles and
empirically using complementary observations.
