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We carry out a detailed characterization of continuous wave threshold behavior of coupled-cavity vertical-cavity surface-emitting lasers with various radii of the ion-implantation and oxide apertures. We obtain modal threshold current maps and wavelength at threshold and identify three groups of lasers with qualitatively different behavior, i.e. 1) lasing only on the short, 2) on both short and long and 3) only on the long wavelength fundamental mode. All lasers show profound impact of the current induced self-heating. In order to elucidate this impact, we improve the existing rate equation model by considering nonuniform longitudinal temperature distribution and adding the gain and refractive index temperature dependencies. We are able to reproduce the experimentally observed switchings between different longitudinal modes, as well as all the three different types of modal behavior.