The `stiffness' of thermal transport in ELMy H-modes is examined in a series of carefully chosen JT-60U plasmas, and measured temperatures are compared with the predictions of several transport models. A heating power scan with constant Tped, a scan of pedestal temperature, Tped, with constant heating power, and an on-axis/off-axis heating comparison are presented. In the power scan, a 45% increase in heating (and a 12% density rise) produces an approximately fixed core temperature profile in a group of five plasmas with the same pedestal temperature. With fixed heating power, we find that a 30–40% increase in Tped is associated with similar increases in core temperature. Heating in the deep core is varied by employing different groups of neutral beams that deposit their power near the magnetic axis and farther from the axis. In these plasmas on-axis heating produces slightly more peaked temperature profiles although they have 60% more heating power inside r = a/2. Transport models are tested by solving the power balance equations to predict temperatures, which are then compared to the measurements. Predictions of the RLWB and IFS/PPPL models generally agree with the measured temperatures outside r∼0.3a, but the Multimode model uniformly predicts temperatures that are too high except in the central region. Tests based on these discharges are not able to discriminate between the transport models of varying stiffness, so we conclude that larger changes are needed in the Pheat and Tped scans.