The Earth has warmed in the last century and a large component of that warming has been attributed to increased anthropogenic greenhouse gases. There are also numerous processes that introduce strong, regionalized variations to the overall warming trend. However, the ability of a forcing to change the surface air temperature depends on its spatial and temporal distribution. Here we show that the efficacy of a forcing is determined by the effective heat capacity of the atmosphere, which in cold and dry climates is defined by the depth of the planetary boundary layer. This can vary by an order of magnitude on different temporal and spatial scales, and so we get a strongly amplified temperature response in shallow boundary layers. This must be accounted for to assess the efficacy of a climate forcing, and also implies that multiple climate forcings cannot be linearly combined to determine the temperature response.