We report the demonstration of a heat-fraction-limited CW Yb:YAG laser operating near 77 K with output at 1029 nm, pumped with a diffraction-limited room-temperature CW Nd:YAG laser operating at 946 nm. With a 50% reflectivity outcoupler, the average threshold absorbed pump power was 18.8 mW and the average slope efficiency 91.9%, close to the heat-fraction limited value of 91.5%. Average optical to optical and photon slope efficiencies are 84% and 100% respectively. To the best of our knowledge this solid-state laser is the first to operate at the heat-fraction-limit and demonstrates record slope, photon slope and optical-optical efficiencies for optically-pumped solid-state lasers.