It has recently been highlighted that the economic value of climate change mitigation depends sensitively on the slim possibility of extreme warming. This insight has been obtained through a focus on the fat upper tail of the climate sensitivity probability distribution. However, while climate sensitivity is undoubtedly important, what ultimately matters is transient temperature change. A focus on transient temperature change stresses the interplay of climate sensitivity with other physical uncertainties, notably effective heat capacity. In this paper we present a conceptual analysis of the physical uncertainties in economic models of climate mitigation, leading to an empirical application of the DICE model, which investigates the interaction of uncertainty in climate sensitivity and the effective heat capacity. We expand on previous results exploring the sensitivity of economic evaluations to the tail of the climate sensitivity distribution alone, and demonstrate that uncertainty about the system’s effective heat capacity also plays a very important role. We go on to discuss complementary avenues of economic and scientific research that may help provide a better combined understanding of the physical and economic processes associated with a rapidly warming world.