We analyzed the output power characteristics of a cryogenically cooled Yb:YAG total-reflection active-mirror (TRAM) laser oscillator including the temperature dependence of the emission cross section and the reabsorption loss of the Yb:YAG TRAM. A CW multi-transverse mode oscillation of a 9.8 at.% doped 0.6 mm thick Yb:YAG ceramic TRAM was investigated for various pump spot sizes and compared with theoretical results. The Yb:YAG temperatures were inferred from the ratio between fluorescence intensities at 1022 nm and 1027 nm which varied significantly with temperature below 200 K. Output power calculations using evaluated temperatures were in good agreement with the experimental data measured between 77 and 200 K, and the output power suppression due to the temperature rise observed above ~140 K. To the best of our knowledge, this is the first evaluation of output power for a cryogenically cooled Yb:YAG TRAM laser.