Greenhouse gas (GHG) additions to Earth’s atmosphere initially reduce global outgoing longwave radiation (OLR), thereby warming the planet. In select environments with temperature inversions, however, increased GHG concentrations can actually increase local OLR. Negative top-of-atmosphere and effective radiative forcing (ERF) from this situation give the impression that local surface temperatures could cool in response to GHG increases. Here we consider an extreme scenario in which GHG concentrations are increased only within the warmest layers of winter near-surface inversions of the Arctic and Antarctic. We find, using a fully coupled Earth system model, that the underlying surface warms despite the GHG addition exerting negative ERF and cooling the troposphere in the vicinity of the GHG increase. This unique radiative forcing and thermal response is facilitated by the high stability of the polar winter atmosphere, which inhibits thermal mixing and amplifies the impact of surface radiative forcing on surface temperature. These findings also suggest that strategies to exploit negative ERF via injections of short-lived GHGs into inversion layers would likely be unsuccessful in cooling the planetary surface. and Note: A revised data description file was added to this work on April 11, 2018 containing additional information about the data set than was provided in the original description. Additional keywords and a full citation to the related article were added as well.