Urban air pollution and climate are closely connected due to shared generating processes (e.g., combustion) for emissions of the driving gases and aerosols. They are also connected because the atmospheric lifecycles of common air pollutants such as CO, NOx and VOCs, and of the climatically important methane gas (CH4) and sulfate aerosols, both involve the fast photochemistry of the hydroxyl free radical (OH). Thus policies designed to address air pollution may impact climate and vice versa. We present calculations using a model coupling economics, atmospheric chemistry, climate and ecosystems to illustrate some effects of air pollution policy alone on global warming. We consider caps on emissions of NOx, CO, volatile organic carbon, and SOx both individually and combined in two ways. These caps can lower ozone causing less warming, lower sulfate aerosols yielding more warming, lower OH and thus increase CH4 giving more warming, and finally, allow more carbon uptake by ecosystems leading to less warming. Overall, these effects significantly offset each other suggesting that air pollution policy has a relatively small net effect on the global mean surface temperature and sea level rise. However, our study does not account for the effects of air pollution policies on overall demand for fossil fuels and on the choice of fuels (coal, oil, gas), nor have we considered the effects of caps on black carbon or organic carbon aerosols on climate. These effects, if included, could lead to more substantial impacts of capping pollutant emissions on global temperature and sea level than concluded here. Caps on aerosols in general could also yield impacts on other important aspects of climate beyond those addressed here, such as the regional patterns of cloudiness and precipitation.