Following the same strategy used for RVO3, thermal conductivity measurements have been made on a series of single-crystal perovskites RTiO3 (R=La,Nd,...,Yb). Results reveal explicitly a transition from an orbital liquid to an orbitally ordered phase at a magnetic transition temperature, which is common for both the antiferromagnetic and ferromagnetic phases in the phase diagram of RTiO3. This spin/orbital transition is consistent with the mode softening at T_{N} in antiferromagnetic LaTiO3 and is supported by an anomalous critical behavior at T_{c} in ferromagnetic YTiO3.