The mode thermo stability conditions for the modes of a conventional linear resonator are developed to apply to a general resonator. The concept of weak thermo stability is introduced, and a new design method,which satisfies both the weak thermo stability conditions for the resonator modes and the thermo stability conditions for the output power, is proposed. With this method, one can make the output power thermo stable and the resonator modes partially thermo stable (for example, the divergence angle can be made thermo stable). Furthermore, analytic solutions to the strong and weak thermo stability conditions for several kinds of resonators are obtained.