A thermo-optical model describing the cavity stability and TEM00-mode volume of a repetitively pumped solid-state laser is developed and verified experimentally. The model predicts a maximum theoretical TEM00 Gaussian-mode radius in the laser rod. This maximum mode radius is caused by a bifocusing of the cavity mode and is present even in gain-polarized materials that nominally suppress the effect of birefringence on beam polarization. The mode limitation effect is not eliminated by conventional optics and is reduced only marginally by the often-described technique of placing a second identical laser head in the cavity. A maximum mode radius implies a fundamental limit on the TEM00-mode energy that can be extracted from a given laser cavity.