The thermal conductivity and the thermal diffusivity of AgPO3 and (AgI)0.5(AgPO3)0.5 glasses have been measured simultaneously in the temperature ranges below and above the glass transitions by using an improved transient hot-wire (multicurrent) method. Using this method, both of the thermal transport properties could be measured accurately. Special care was taken in the measurement concerning the high ionic conductivity of the materials. The temperature dependences of the two transport properties were especially noted, and apparent differences in them could be seen between the two glassy materials. The experimental results were discussed on the basis of a simple phonon transport theory with special consideration of the present superionic conducting glasses.