In this work we report thermal conductivity measurements on the heavy fermion superconductors PrOs4Sb12 (Tc~1.75K) and CeCoIn5 (Tc~2.35K). After an introduction to these compounds, particular emphasis is put on the experimental technique, which has allowed reliable measurements down to 10mK and in magnetic fields up to 6.5T. As an original part of this work, we developed a method to fully characterize (quantitatively) the electric thermal contact resistances on the setup. A strong increase in the low temperature field dependence of thermal conductivity in PrOs4Sb12 and CeCoIn5 reveals the existence of a characteristic field scale much smaller than the upper critical field Hc2. This high field sensitivity of heat transport does not correspond to predictions for ordinary type II or unconventional superconductors with gap nodes, but rather supports a multigap superconductivity scenario, reminiscent of the case of MgB2. Moreover, in PrOs4Sb12, the temperature dependence of thermal conductivity points to fully open gaps on the whole Fermi surface, whereas strong suppression of inelastic scattering impedes any conclusion on the gap topology on CeCoIn5.