Climate studies often assume that a key metric of global warming, the equilibrium climate sensitivity (∆T2x,eq, the long-term warming from doubling atmospheric CO2), is constant, and that it has the same value as the instantaneous climate sensitivity (∆T2x,inst, an estimate of ∆T2x,eq made using time series of surface temperature and net top-of-atmosphere radiative flux). Recent studies have shown that both assumptions should be reconsidered: in computer simulations, ∆T2x,eq can depend on the background state under anthropogenic levels of forcing, and ∆T2x,inst often differs from ∆T2x,eq. These discrepancies suggest that past estimates of climate sensitivity and of future warming may be incorrect. In this thesis, we explore the causes of these two discrepancies and develop new models that account for them, allowing for more accurate forecasting of future warming. We explore the first issue by extending a simple energy balance model to account for the fact that the feedback processes that determine the climate sensitivity can change strength in a warmer world, causing ∆T2x,eq to vary. We use a measure of this feedback temperature dependence, a, to show that positive values of a predict the large increases in ∆T2x,eq under successive doublings of CO2 seen in some general circulation models (GCMs). Using this simple model, we show that the range of values of a seen in GCMs implies that observational probabilistic forecasts of climate sensitivity underestimate the risk of high warming. The degree of this underestimate depends on how sensitive the planet is initially. We perform offline calculations on the ECHAM6.1 model to demonstrate that changes in equilibrium climate sensitivity are partly driven by feedback temperature dependence through increases in the water vapor feedback. Perturbing the convective parameters in ECHAM6.1 demonstrates that a small uncertainty in present day climate sensitivity can translate into large uncertainties in sensitivity at higher forcings when a is positive. We explore the second discrepancy by developing an energy balance model that accounts for the spatially nonuniform nature of the Earth's radiative feedbacks (the primary cause in the difference between ∆T2x,eq and ∆T2x,inst). We demonstrate a method for estimating these spatial radiative feedbacks from interannual variability by using multiple regression of top-of-atmosphere fluxes against local and non-local surface temperature. Our method can separate the global feedback into local and nonlocal components, and we show that most models have strong negative nonlocal feedbacks associated with warming in regions of tropical convection. Since warming is initially more weighted towards the tropics, these negative feedbacks make initial values of ∆T2x,inst lower than ∆T2x,eq. These two issues are compounding, in that if we are underestimating the ∆T2x,eq associated with the present climate due to spatially varying feedbacks, this makes it much more likely that we are underestimating the value ∆T2x,eq will have in the warmer future due to feedback temperature dependence. While the chapters of this thesis use results from computer simulations of climate to assess the power of these effects, they also point towards ways that observations and physical reasoning can be used to measure their strength. Regardless of the method, the present work makes clear that we must account for these two causes of time-varying climate sensitivity to properly forecast future warming.