Towards fabricating a thermoelectric power device using III-nitrides and III-oxynitrides, we studied their thermal and thermoelectric properties and, in particular, we have focused on their thermal conductivity. AInN and AlInON were prepared by reactive radio-frequency sputtering method. We measured the thermal diffusivity and specific heat using the ac calorimetric method, and we estimated values of the thermal conductivity to be 2.2 W/mK (at 773 K) for AlInN and 3.3 W/mK (at 673 K) for AlInON. These values are much smaller than expected considering the large thermal conductivity of nitrides. As for a device composed of 20-pair Chromel-AlInN films, the maximum output power was 0.36 μW at the temperature difference of 180 K, and the open voltage was 0.10 V.