We have measured the thermal conductivity in the ab-plane and along the c-axis, κ(subscript ab)(T) and κ(subscript c) (T), for the large single crystallines of RE2CuO4 (RE=Pr, Nd, and Sm). A double-peak structure which originated from the phonon and magnon contributions was found in κ(subscript ab)(T) for all the RE2CuO4 single crystals. The magnon peak in κ(subscript ab)(T) strongly depends on the species of RE. We found a very large magnon contribution in Sm2CuO4. This can be explained by the interaction between the Sm and Cu moments. κ(subscript c)(T) of Sm2CuO4 also showed an anomalous large peak around 25 K.