Novel high-power ytterbium YAG lasers are described. These lasers incorporate the principle of anti-Stokes fluorescence cooling to reduce or eliminate detrimental heating. Lasers with net heating and net cooling are demonstrated. By balancing the spontaneous and stimulated emission, we have reduced the net thermal loading to below 0.01% of the laser's average output power. Design, testing, and analysis are reported for lasers up to 500 W average power and pulsed operation up to 30 s. Issues and limitations of this approach are discussed.