Natural unforced variability in global mean surface air temperature (GMST) can mask or exaggerate human-caused global warming, and thus a complete understanding of this variability is highly desirable. Significant progress has been made in elucidating the magnitude and physical origins of present-day unforced GMST variability, but it has remained unclear how such variability may change as the climate warms. Here we present modelling evidence that indicates that the magnitude of low frequency GMST variability is likely to decline in a warmer climate and that its generating mechanisms may be fundamentally altered. In particular, a warmer climate results in lower albedo at high latitudes, which yields a weaker albedo feedback on unforced GMST variability. These results imply that unforced GMST variability is dependent on the background climatological conditions, and thus climate model control simulations run under perpetual pre-industrial conditions may have only limited relevance for understanding the unforced GMST variability of the future.