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It has been previously shown that it is theoretically possible to build a solid-state laser that generates no internal heat. This is accomplished through a detailed balance of the stimulated and spontaneous emission. Such a device is called a radiation-balanced laser. Here, we analyze laser operation when conditions deviate from perfect balance. Sensitivity and stability analyses are presented for perturbations in the field parameters and temperature. We show that the radiation balance is a stable equilibrium under both transient and steady-state perturbations. Limits are derived on the magnitude of allowable spatial perturbations, and techniques for spatial mode matching are discussed. Numerical simulations of 1-μm laser operation of Yb-doped potassium gadolinium tungstate are provided as an example.