Measurements of the in-plane (kappa(ab)) and out-of-plane (kappa(c)) t
hermal conductivity for insulating cuprate crystals are discussed alon
g with new measurements for YBa2Cu3O6 and PrBa2Cu3O6, where both kappa
(ab) and kappa(c) are twice the magnitude previously reported for this
material. An unusual temperature (T) dependence of kappa(ab) in cupra
tes with apical oxygen indicates the onset of strong phonon damping fo
r T < 200-250K. Along with dielectric and elastic anomalies reported i
n this regime, the data suggest the occurrence of a structural phase t
ransition, involving rotations of the CuO polyhedra about an in-plane
axis. The role of such local distortions in the thermal transport of s
uperconducting compounds and the superconducting-state enhancement of
kappa(ab) are discussed.