We quantify the temperature-dependence of the clear-sky climate sensitivity in a one-dimensional radiative-convective equilibrium model. The atmosphere is adjusted to fixed surface temperatures between 280 and 320 K while preserving other boundary conditions in particular the relative humidity and the CO2 concentration. We show that an out-of-bounds usage of the radiation scheme RRTMG can lead to an erroneous decrease of the feedback parameter and an associated “bump” in climate sensitivity as found in other modelling studies. Using a line-by-line radiative transfer model, we find an almost constant longwave radiative feedback at surface temperatures above 300 K. However, the line-by-line simulations also show a slight decrease in climate sensitivity when surface temperatures exceed 310 K. This decrease is caused by water-vapor masking the radiative forcing at the flanks of the CO2 absorption band, which reduces the total radiative forcing by about 18%.