Thin-disk laser experiments with Yb:CaGdAlO(4) (Yb:CALGO) have been performed. A slope efficiency of 70% and an optical-to-optical efficiency of 57% could be achieved with a maximum output power of 30.7 W. These are so far the highest efficiencies obtained with this material. Furthermore, tuning experiments were carried out leading to a tuning range of 90 nm in total and 50 nm with more than 20 W of output power. This is to the best of our knowledge the widest wavelength tuning range of any material demonstrated at this power level. For all experiments the thermal evolution of the crystal surface temperature during laser operation was investigated.