We monitor the time evolution of the temperature of phononic collective modes in a one-dimensional quasicondensate submitted to losses. At long times the ratio between the temperature and the energy scale mc2, where m is the atomic mass and c the sound velocity takes, within a precision of 20%, an asymptotic value. This asymptotic value is observed while mc2 decreases in time by a factor as large as 2.5. Moreover this ratio is shown to be independent on the loss rate and on the strength of interactions. These results confirm theoretical predictions and the measured stationary ratio is in quantitative agreement with the theoretical calculations