Recently, the thermo-optic effect, which causes refractive index change in active optical fibers, emerged as one of the most limiting factor to power scaling of fiber lasers. The thermally-induced refractive index gradient in the fiber cross-section jeopardizes the extreme guiding properties required to obtain single-mode propagation in ultra Large Mode Area (LMA) fibers, eventually causing the rise of mode instabilities. In this paper the resilience to thermal effects of different rod-type Double Cladding Photonic Crystal Fiber designs, namely the 19-cell core, the distributed modal filtering and the large-pitch PCFs, have been compared through numerical simulations. The single-mode properties of each fiber have been obtained for different heating conditions. The causes of the different behavior have been investigated, providing a detailed overview of the influence of thermo-optical effects on the guiding properties of LMA PCFs, as well as some guidelines for the design of LMA PCFs for high-power applications.