The electrical resistivity rho(T) and the thermal conductivity lambda(T) have been measured for UCu5 in the temperature range between 0.02 and 20 K. Two distinct anomalies in rho(T) are due to previously established phase transitions at approximately 15 and 1 K, respectively. They indicate considerable changes in the electronic structure of this compound, implying sizeable truncations of the Fermi surface with decreasing temperature at both transitions. In almost the entire covered temperature range the thermal conductivity is dominated by phonon contributions. Its temperature dependence is fairly well reproduced by a calculation considering phonon scattering by electrons and by point defects, At very low temperatures, as T approaches 0 K, the Wiedemann-Franz law lambda(e) . rho = L0 T, where lambda(e) is the electronic part of lambda(T) and L0 is the Lorenz number, is almost perfectly fulfilled.