The absorption coefficients of nonlinear crystals for fundamental and second harmonic wave are of great importance for high average power second harmonic generation. A practical method to measure low absorption coefficients is to use an interferometric laser calorimeter with high power lasers. Therefore Q-switched Nd:YAG laser systems with intracavity second harmonic generation are used. The measurements are made with optical powers up to 300 W (1064 nm) and 45 W (532 nm), respectively. Because of the high power, the resolution limit for the absorption coefficients is 0.001 %/cm. The absorption coefficients of KTP and LBO crystals of different manufacturers are determined. The results are used for a numerical model which takes into account the decrease of conversion efficiency due to thermal effects caused by the absorption of laser power in the nonlinear crystal. This model describes saturation effects which appear in the range of 100 W in the green using a KTP crystal. A new idea for compensation of thermal effects will be presented.