We demonstrate a high-efficiency, high-average-power, CW master oscillator power amplifier based on a conduction-cooled, end-pumped Yb:YAG slab architecture at room temperature (RT). Firstly, the CW amplification property is theoretically analyzed based on the kinetics model for Yb:YAG. To realize high-efficiency laser amplification extraction for RT Yb:YAG, not only intense pump but also a high-power seed laser is of great importance. Experimentally, a composite Yb:YAG crystal slab with three doped and two un-doped segments symmetrically is employed as the gain medium, which is end-pumped by two high-power, 940-nm diode lasers. A high-power, narrow-spectral-width, 1030-nm fiber seed laser then double passes the composite slab to realize efficient power amplification. For 0.8-kW seed input, maximum output power of 3.54 kW is obtained at 6.7 kW of pump power, with the optical conversion efficiency of 41% and the highest slope efficiency of 59%. To the best of our knowledge, this is the highest power and efficiency reported for Yb:YAG lasing at RT except thin-disk lasers.