  We study the low-temperature heat transport in clean two-leg spin ladder
compounds coupled to three-dimensional phonons. We argue that the very large
heat conductivities observed in such systems can be traced back to the
existence of approximate symmetries and corresponding weakly violated
conservation laws of the effective (gapful) low--energy model, namely
pseudo-momenta. Depending on the ratios of spin gaps and Debye energy and on
the temperature, the magnetic contribution to the heat conductivity can be
positive or negative, and exhibit an activated or anti-activated behavior. In
most regimes, the magnetic heat conductivity is dominated by the spin-phonon
drag: the excitations of the two subsystems have almost the same drift
velocity, and this allows for an estimate of the ratio of the magnetic and
phononic contributions to the heat conductivity.
