We explore the thermo-optical issues of mode-matched end-pumped lasers. A combination of analytical and numerical methods is used to extract practically useful scaling relations that characterize the thermally induced optical distortions and the thermal-stress operating limits in rod lasers pumped with super-Gaussian sources. The thermally induced spherical aberration is found to be overcorrected (focal length increases with radial position), weakly dependent on the axial profile, and strongly dependent on the super-Gaussian order. For high-order radial profiles it is shown that a significant portion of the extraction beam will operate aberration free. The effect of aberrations on cavity stability is addressed for the simple case of a cavity with a length that is equal to the rod length.