The climatological impact of increases in greenhouse gas concentrations in the atmosphere, despite being a subject of intensive study in recent years, is still very uncertain. One major uncertainty affecting possible climate change that has not received enough attention is the uncertainty in heat uptake by the deep ocean. We analyze the influence of this process and its uncertainty on climate predictions by means of numerical simulations with a 2-dimensional climate model. In the case of high climate sensitivity, as a result of uncertainty in deep ocean heat uptake, there is more than a factor of two uncertainty in the predicted increase of surface temperature. The corresponding uncertainty in the sea level rise due to thermal expansion is much larger than the uncertainty in the predicted temperature change and is significant even in the case of low climate sensitivity.