Although emission controls for greenhouse gases may limit their future rise, there is a finite chance that a substantial fraction of the available fossil fuel reservoir will be utilized. Geochemical models suggest that the atmospheric perturbation would then last for thousands of years. We use a well-calibrated energy balance model, coupled to an upwelling-diffusion deep-ocean model, to estimate the temperature effects of such unrestricted emissions. We calculate that greenhouse warming will peak between ~2200--2400, with a global temperature increase 4--13 ¿C greater than present. The high-end estimate is as much as 100% larger than estimates of the temperature increase for the ice-free Cretaceous (100 Ma) warm period. Warming of as much as 2--5 ¿C persists as late as 10,000 years AP. The ''out-year'' projections are larger than Milankovitch effects occurring over the same interval, indicating that unrestricted emissions could lead to conditions in which anthropogenic warming dominates climate variation for the next 10,000 years.