Lateral leakage of light has been identified as a detrimental loss source in many suggested and experimentally realized GaN-based VCSELs. In the present work we include thermal effects to realistically account for the substantial Joule heating in these devices. In contrast to what could be expected from the previous results, the induced thermal lensing does not make antiguided cavities more positively guided, so that they approach the unguided regime with extremely high lateral leakage. Rather, thermal lensing strongly suppresses lateral leakage for both antiguided and guided cavities. This is explained in terms of lowered launch of power from the central part of the cavity and/or lower total internal reflection in the peripheral part; the former effect is active in all cavities whereas the latter only contributes to the very strongly reduced leakage in weakly antiguided cavities. Thermal lensing suppresses lateral leakage both for the fundamental and the first higher order mode, but a strong modal discrimination is still achieved for the antiguided cavities. Thus, strongly antiguided cavities could be used to achieve single-mode devices, but at the cost of slightly higher threshold gain and stronger temperature dependent performance characteristics.