Few-layer InSe as a newly emerged two-dimensional transition metal dichalcogenide (TMD) has attracted a great interest due to its high carrier mobility and broad absorption spectrum. However, InSe is more easily oxidized as exposed to the ambient atmosphere than other TMDs and its thermal stability has not been carefully studied until now. In this work, we systematically study the thermal evolution of InSe in air via optical microscopes, Raman, XPS and PL spectra, as well as AFM measurements. It has been demonstrated that such thermal evolution can be decomposed into three stages, including oxygen adsorption on the surface at low temperature, InSe1-xOx formation on the surface at mediate temperature and final In2O3 formation at high temperature. We also compare the thermal stability between pure InSe, InSe covered by graphene and InSe protected by h-BN. The pure InSe is completely destroyed at similar to 450 degrees C, whereas InSe covered by graphene is more stable until similar to 540 degrees C, and the sample protected by h-BN remains stable even at similar to 620 degrees C. This work may offer a clear physical picture of the oxidation process of InSe in air and be helpful for the application of InSe based optoelectronic devices.