A new algorithm is proposed for estimating time-evolving global forcing in climate models. The method is a further development of the work of Forster et al. (2013), taking into account the non-constancy of the global feedbacks. We assume that the non-constancy of this global feedback can be explained as a time-scale dependence, associated with linear temperature responses to the forcing on different time scales. With this method we obtain stronger forcing estimates than previously assumed for the representative concentration pathway experiments in the Coupled Model Intercomparison Project Phase 5 (CMIP5). The reason for the higher future forcing is that the global feedback parameter is more negative at shorter time scales than at longer time scales, consistent with the equilibrium climate sensitivity increasing with equilibration time. Our definition of forcing provides a clean separation of forcing and response, and we find that linear temperature response functions estimated from experiments with abrupt quadrupling of CO$_2$ can be used to predict responses also for future scenarios. In particular, we demonstrate that for most models, the response to our new forcing estimate applied on the 21st century scenarios provides a global surface temperature up to year 2100 consistent with the output of coupled model versions of the respective model.