Reductions in anthropogenic aerosol emissions will cause a near-term warming of climate that will impact our trajectory towards 1.5℃, the target set by the Paris Agreement to limit global temperature rise since pre-industrial levels to. There is persistent uncertainty in aerosol radiative forcing that limits our understanding of exactly how the climate will respond to near-term reductions in anthropogenic aerosol emissions. We calculate global mean aerosol radiative forcing up to 2050 for emissions scenarios consistent with the Shared Socioeconomic Pathways (SSPs). We use statistical techniques to quantify the model uncertainty in near-term projections of aerosol radiative forcing due to the uncertainty in aerosol emission, process and removal parameters in a global climate model. A simple model is then used to translate our uncertainty in aerosol radiative forcing to temperature projections. Our global mean aerosol radiative forcing at 2050 relative to 2000 for a middle of the road emissions scenario (SSP2-RCP4.5) has a credible interval of 0.59-1.01 W m-2, representing model parametric uncertainty. The scenario uncertainty in aerosol radiative forcing at 2050 is 0.30-1.12 W m-2 for three scenarios that span differing strengths of air quality policies. The spread in aerosol radiative forcing due to parametric model uncertainty in a single emission scenario (SSP2-RCP4.5) alone creates a 5-year window on the projected exceedance year of a mean climate global temperature rise of 1.5℃. This spread in exceedance year of 1.5℃ due to aerosol radiative forcing uncertainty is comparable to the projected time window due to the uncertainty in Equilibrium Climate Sensitivity (ECS).