The role of thermal instability and In surface coverages on the growth kinetics has been investigated for N-face InN films grown by plasma-assisted molecular beam epitaxy. Film thickness analysis using scanning electron microscopy combined with In desorption measurements by quadrupole mass spectrometry demonstrated significant thermal decomposition starting at ∼560°C and inhibiting growth completely beyond ∼635°C. Within this temperature region two decomposition pathways were identified: a low-temperature regime characterized by In droplet accumulation and a high-temperature regime with direct desorption from bulk InN. A growth diagram has been constructed, exhibiting three characteristic growth structures for different In/N flux ratios and growth temperatures: a dry no-adlayer terminated surface under N-rich conditions, an In adlayer terminated surface, and a surface, consisting of an In adlayer and droplets under In-rich conditions. Smooth step-flow growth terraces were observed in films grown under In-rich and surprisingly also under N-rich conditions at temperatures of thermal decomposition. Such high adatom diffusivity resulted from the autosurfactant action of the In adlayer, with a saturated coverage of 1 ML as determined from the reflection high energy electron diffraction patterns during the consumption of adsorbed In by active nitrogen.