Warming in climate-change simulations reaches a local maximum in the tropical upper troposphere as expected from moist-adiabatic lapse rates. But the structure of warming varies between models and differs substantially from moist adiabatic in the extratropics. Here, we relate the vertical profile of warming to the climatological temperature profile using the vertical-shift transformation (VST). The VST captures much of the intermodel scatter in the ratio of upper- to middle-tropospheric warming in both the extratropics and tropics of simulations from the Coupled Model Intercomparison Project 5 (CMIP5). Application of the VST to observed climatological temperatures yields warming ratios that are in the range of what is obtained from the model climatological temperatures, although biases in some model climatologies lead to substantial errors when shifted upward. Radiosonde temperature trends are consistent with an upward shift in recent decades in the Northern Hemisphere, with less-robust results in the Southern Hemisphere.