Radiation-balanced lasing and thermal profiling is reported in two Yb-doped laser crystals at room temperature. In 3% Yb3+:YAG a record efficiency of 30.5% was achieved by frequency-locking the laser cavity to the input light. Both the average excursion and axial temperature gradient of the gain medium were maintained within 0.1 K of room temperature at the radiation balance point. By including saturation of background impurity absorption in the analysis, quantitative agreement was obtained between theory and the experimentally measured laser threshold, radiation balance condition, output wavelength, and laser efficiency with only one free parameter. Radiation-balanced lasing was also achieved in 2% Yb3+:KYW with an efficiency of 2.2% despite high background impurity absorption, losses from Brewster end faces that were not parallel, and non-optimal output coupling. Our results confirm that relatively impure gain media can be operated as radiation-balanced lasers, contrary to earlier predictions which ignored background impurity properties.