Thermal lensing poses a serious challenge for the power scaling of enhancement cavities, in particular when these contain transmissive elements. We demonstrate the compensation of the lensing induced by thermal deformations of the cavity mirrors with the thermal lensing in a thin Brewster plate. Using forced convection to fine-tune the lensing in the plate, we achieve average powers of up to 160 kW for 250-MHz-repetition-rate picosecond pulses with a power-independent mode size. Furthermore, we show that the susceptibility of the cavity mode size to thermal lensing allows highly sensitive absorption measurements.