Abstract: We have measured the thermal conductivity of ceramic samples of TlBaCaCuO between 2 and 250 K. At high temperatures it follows a constant behaviour down to the superconducting transition temperature where a sudden increase of the thermal conductivity occurs, attributed to reduced phonon scattering by condensating electrons. At low temperatures a T2 law is observed, confirming the assumption that it is a common feature in most of the high temperature superconducting oxides. Phonon scattering against tunneling systems analogous to those found in amorphous solids can explain this behaviour.