  We find a simple exact model of radiating stellar collapse, with a shear-free
and non-accelerating interior matched to a Vaidya exterior. The heat flux is
subject to causal thermodynamics, leading to self-consistent determination of
the temperature $T$. We solve for $T$ exactly when the mean collision time
$\tau_{c}$ is constant, and perturbatively in a more realistic case of variable
$\tau_{c}$. Causal thermodynamics predicts temperature behaviour that can
differ significantly from the predictions of non-causal theory. In particular,
the causal theory gives a higher central temperature and greater temperature
gradient.
