This paper analyses the policy relevance of the dominant uncertainties in our current scientific understanding of the terrestrial climate system, and provides further evidence for the need to radically transform - this century - our global infrastructure of energy supply, given the global average temperature increase as a result of anthropogenic carbon dioxide emissions. We investigate the effect on required CO2 emission reduction efforts, both in terms of how much and when, of our uncertain knowledge today of the climate sensitivity to a doubling in them atmospheric CO2 concentration. Also the roles of carbon-free energy and energy savings, and their evolutions over time, are researched, as well as their dependence on some of our characteristic modelling features. We use a top-down model in which there are two competing energy sources, fossil and non-fossil. Technological change is represented endogenously through learning curves, and modest but non-zero demand exists for the relatively expensive carbon-free energy resource.