The thermally conductive composite oxide of the present invention has excellent physical properties, such as high thermal conductivity, water resistance, acid resistance, electric resistance, and electric insulation, required for coating films, films, and articles thereof. Paints or resins including the composite oxide can provide coating films, films, and articles having such properties without treating of a surface, etc. The composite oxide has a spinel structure and contains aluminum as a main metal component and at least one metal other than aluminum, which is magnesium, zinc, calcium, and/or strontium, and has a ratio (b mol)/(a mol) in a range of 0.1 or more and 1.0 or less, where the ratio (b mol)/(a mol) is a number of moles (b) of the metal other than aluminum to that of moles (a) of an aluminum element derived from an alumina-based compound. The thermally conductive composite oxide has Mohs hardness of less than 9.