We theoretically and experimentally examine thermal oscillations in a calcium fluoride whispering-gallery-mode resonator that lead to strong mode-frequency oscillations. We show that these oscillations arise from interplay among thermal expansion, the thermo-optic effect, and Kerr effects. In certain regimes we observe chaotic behavior and demonstrate that the threshold for this behavior can be predicted theoretically. We then demonstrate a self-stabilization technique that suppresses the oscillations and delivers high temperature and frequency stability without reference to external standards.