Thermal diffusion, thermal conductivity, and heat capacity of Bi1-xRexFeO3 multiferroics (Re – rare-earth element; х = 0 - 0.20) are investigated in the temperature interval of 130 K to 1200 K. The rare earth substitution leads to a change in the temperature anomalies of the thermal diffusion and conductivity and in antiferromagnetic phase transition region, the increase of the heat capacity in a wide temperature range, and the temperature displacement of the antiferromagnetic transition. It is established that the temperature dependence of the excess heat capacity is associated with the Schottky effect for three states of the level resulting from structure distortions in the rare-earth-doped compositions. The analysis of the results along with structural and acoustic data indicates that local distortions of the crystal lattice, which are caused by the distortions of oxygen octahedra of FeO6 and polar shifts of Bi3+ and Fe3+ ions from their initial positions, constitute the main mechanism of the scattering of phonons in BiFeO3 and Bi1-xRexFeO3 multiferroics. It is found that Re doping leads to a significant change in the temperature anomalies of the thermal diffusion and thermal conductivity near phase transitions, namely, to the smearing of the ferroelectric transition Tc and the appearance of a minimum in the region of the antiferromagnetic transition TN. The dominant mechanisms of phonon heat transfer in the region of ferroelectric and antiferromagnetic phase transitions are revealed. The temperature dependence of the mean free path of phonons is determined.