We unveil a gas-lens effect in kW-class thin-disk lasers, which accounts in our experiments for 33% of the overall disk thermal lensing. By operating the laser in vacuum, the gas lens vanishes. This leads to a lower overall thermal lensing and hence to a significantly extended power range of optimal beam quality. In our high-power continuous-wave (cw) thin-disk laser, we obtain single-transverse-mode operation, i.e. M2 < 1.1, in a helium or vacuum environment over an output-power range from 300 W to 800 W, which is 70% broader than in an air environment. In order to predict the magnitude of the gas-lens effect in different thin-disk laser systems and gain a deeper understanding of the effect of the heated gas in front of the disk, we develop a new numerical model. It takes into account the heat transfer between the thin disk and the surrounding gas and calculates the lensing effect of the heated gas. Using this model, we accurately reproduce our experimental results and additionally predict, for the first time by means of a theoretical tool, the existence of the known gas-wedge effect due to gas convection. The gas-lens and gas-wedge effects are relevant to all high-power thin-disk systems, both oscillators and amplifiers, operating in cw as well as pulsed mode. Specifically, canceling the gas-lens effect becomes crucial for kW power scaling of thin-disk oscillators because of the larger mode area on the disk and the resulting higher sensitivity to the disk thermal lens.