Forecasting the future sea level relies on accurate modeling of the response of the Greenland and Antarctic ice sheets to changing temperatures. We show why the steady state of an ice sheet is biased toward larger size if the interannual weather generated fluctuations in temperature are not taken into account in numerical modeling of the ice sheet. We illustrate this in a simple ice sheet model. This bias could, if not taken into account, imply that the risk of collapse in a given climate change scenario is underestimated. We estimate that the effect of temperature variability on the surface mass balance of the Greenland Ice Sheet in recent ensemble forecasting should be adjusted downward by approximately 13 percent of the present day observed value, if assuming a 2 degree warming. Many predicted scenarios of the future climate show an increased variability in temperature over much of the Earth. In light of our findings it is important to gauge the extent to which this increased variability will further influence the mass balance of the ice sheets.