We present thermal conductivity measurements in short period GaAs/AlAs superlattices. The aim of this study is to get a better understanding of the various processes which restrict the phonon transport in semiconductor superlattices. In particular, the role of interface scattering is still under debate and very few experiments have been devoted to address this issue. Using the so-called 3w method, we measured the cross-plane thermal conductivity, of (GaAs)n(AlAs)n where n=3, 8 and 20. The interface roughness is controlled thanks to the growth temperature of the samples. We also present and discuss results as a function of temperature, between 20 and 300 K. For a given period, no significant change as a function of interface roughness is observed. Recent molecular dynamic simulations, using realistic interface models, could give clues to this low sensitivity versus interface quality.