The oxidation of InAs(001) surfaces under UV-generated ozone and thermal desorption of the oxide layers under an As pressure was investigated by in situ reflection high-energy electron diffraction (RHEED), XPS, and STM, as well as by ex situ TEM and AFM. Amorphous oxide layers of up to 3 nm thickness were produced at room temperature, and consisted in As2O3, As2O5, and In2O3, as well as some atomic As at the interface between oxide and substrate. During heating to about 300 degrees C, the As-oxides desorbed, together with the initially present carbonaceous contamination, while In2O3 recrystallized, partly in epitaxial orientation on the substrate. Most of the In-oxide islands evaporated upon heating to 480 degrees C. A short time heat pulse to about 580 degrees C resulted in complete desorption of the remaining oxide islands, while more gradual heating caused decomposition of the InAs and formation of In droplets. It is demonstrated that UV/ozone oxidation and controlled oxide desorption yields clean, stoichiometric and reasonably flat surfaces, which are suitable for molecular beam epitaxy (MBE) growth of InAs layers and heterostructures.