This paper investigates the sound absorption properties of porous composites with solid impervious heated inclusions, i.e. heat sources, which allow the temperature tuning of the porous constituents and the control of the pressure diffusion phenomenon. By means of the two-scale asymptotic method of homogenisation, the wave equation in the composites with heated impervious inclusions is derived, allowing the material to be modelled as an equivalent fluid with effective density and compressibility. Analytical and semi-analytical models for the acoustical properties of porous composites with inclusions of different geometries are developed, which are also numerically validated using the finite element method. This work demonstrates that adjusting the temperature of the porous constituents can provide an alternative way of controlling the absorptive properties of hard-backed porous composite layers, and highlights the dependence of pressure diffusion on temperature.