N-face {0001} InN films, grown by plasma-assisted molecular beam epitaxy on sapphire (0001) and Si (111) substrates were annealed in a nitrogen atmosphere, with the aim to determine the limits of their thermal stability and look into the degradation of their optoelectronic properties. Indium clusters, indicating InN decomposition, were observed after annealing at 500 degrees C on the film grown on sapphire, while they were present already after annealing at 450 degrees C on the film grown on Si. The disintegration of InN films occurred after annealing at 500 degrees C by through-holes formation, and it was enhanced by cracking and delamination on the Si substrate. A significant deterioration of electron Hall mobility was observed after annealing at 500 degrees C and it correlated with the extent of disintegration of each film. Both as-grown and annealed films exhibited broad PL spectra, typical for heavily doped semiconductors, with films on the Si substrate exhibiting non-uniformities of PL spectra throughout the surface. The evolution of the PL spectra correlated with the signatures of annealing-caused crystal deterioration observed by other characterisation techniques, and led to similar PL spectra after annealing at 550 degrees C. The results suggest that InN decomposition is avoided in the films grown on the sapphire substrate if they are annealed at temperatures up to 450 degrees C. InN grown on the silicon substrate exhibits a slightly faster destruction. The findings indicate correlation between the thermal stability and the defect content of the layers and heteroepitaxial interfaces.