Thermal properties of InP-based quantum well photonic crystal nanobeam lasers heterogeneously integrated on silicon on insulator waveguides are studied. We show both numerically and experimentally the reduction of the thermal resistance of the III-V cavities by adjusting the composition of the layer which bonds the III-V materials to the silicon wafer and by adding an over-cladding on top of the cavities. Using a bonding layer made of benzocyclobutene and SiO(2) and an over-cladding of MgF(2), we found a decrease by a factor higher than 35 compared to air-suspended photonic crystal nanobeam cavities. Such optimized structures are demonstrated to operate under continuous wave pumping for several 10's of minutes despite the adverse effect of non-radiative surface recombination of carriers.