  We have measured the thermal heat conductivity kappa of the compounds
Sr_14Cu_24O_41 and Ca_9La_5Cu_24O_41 containing doped and undoped spin ladders,
respectively. We find a huge anisotropy of both, the size and the temperature
dependence of kappa which we interpret in terms of a very large heat
conductivity due to the magnetic excitations of the one-dimensional spin
ladders. This magnon heat conductivity decreases with increasing hole doping of
the ladders. The magnon heat transport is analyzed theoretically using a simple
kinetic model. From this analysis we determine the spin gap and the temperature
dependent mean free path of the magnons which ranges by several thousand
angstroms at low temperature. The relevance of several scattering channels for
the magnon transport is discussed.
