The impact of thermally-induced refractive index changes on the single-mode (SM) properties of large mode area (LMA) photonic crystal fibers are thoroughly investigated by means of a full-vector modal solver with integrated thermal model. Three photonic crystal fiber designs are taken into account, namely the 19-cell core fiber, the large-pitch fiber (LPF) and the distributed modal filtering (DMF) fiber, to assess the effects of the interplay between thermal effects and the high-order mode (HOM) suppression mechanisms exploited in order to obtain effectively SM guiding. The results have shown significant differences in the way the SM regime is changed by the increase of heat load, providing useful hints for the design of LMA fibers for high power lasers.