We address the power scaling issue in end-pumped laser rod amplifiers by studying, experimentally and numerically, the magnitude of thermal lensing in a high-energy diode-pumped Yb:YAG crystal. The spatio-temporal temperature profile of the gain medium and the focal length of the induced thermal lens are determined numerically. The influence of the repetition rate and pumping power on the temperature distribution is analyzed. Experimental measurements covered repetition rates between 1 and 10 Hz and up to 4 kW pumping power.