We explore the extent to which internal variability can reconcile discrepancies between observed and simulated warming in the upper tropical troposphere. We compare all extant radiosonde‐based estimates for the period 1958–2014 to simulations from the Coupled Model Intercomparison Project phase 5 multimodel ensemble and the 100 realization Max Planck Institute large ensemble. We consider annual mean temperatures and all available 30‐and 15‐year trends. Most observed trends fall within the ensemble spread for most of the record, and trends calculated over 15‐year periods show better agreement than 30‐year trends, with generally larger discrepancies for the older observational products. The simulated amplification of surface warming aloft in the troposphere is consistent with observations, and the linear correlation between surface and simultaneous tropospheric warming trends decreases with trend length. We conclude that trend differences between observations and simulations of tropical tropospheric temperatures are dominated by observational uncertainty and chaotic internal variability rather than by systematic errors in model performance. Key Points Radiosonde observations show good agreement with a single‐model 100 member ensemble of simulations for the majority of observational record Largest trend differences for amplification of tropospheric over surface warming aloft for 30‐year trends occur in second half of the record Differences in observed and simulated tropical tropospheric temperature trends arise from observational uncertainty and internal variability