  High-resolution imaging of protoplanetary disks has unveiled a rich diversity
of spiral structure, some of which may arise from disk-planet interaction.
Using 3D hydrodynamics with $\beta$-cooling to a vertically-stratified
background, as well as radiative-transfer modeling, we investigate the
temperature rise in planet-driven spirals. In rapidly cooling disks, the
temperature rise is dominated by a contribution from stellar irradiation,
0.3-3% inside the planet radius but always <0.5% outside. When cooling time
equals or exceeds dynamical time, however, this is overwhelmed by hydrodynamic
PdV work, which introduces a 10-20% perturbation within a factor of 2 from the
planet's orbital radius. We devise an empirical fit of the spiral amplitude
$\Delta (T)$ to take into account both effects. Where cooling is slow, we find
also that temperature perturbations from buoyancy spirals -- a strictly 3D,
non-isothermal phenomenon -- become nearly as strong as those from Lindblad
spirals, which are amenable to 2D and isothermal studies. Our findings may help
explain observed thermal features in disks like TW Hydrae and CQ Tauri, and
underscore that 3D effects have a qualitatively important effect on disk
structure.
