First results of heat wave propagation experiments in plasmas with Internal Transport Barriers (ITBs) were obtained in JET. These showed that ITBs are narrow layers and induce strong damping and slowing down of the heat wave. This implies a very low perturbed heat diffusivity, indicating a transport regime which is sub-critical with respect to turbulence thresholds. In this paper more analysis is presented of an extended database of JET ITB discharges with ICH power modulation in Mode Conversion (in D2 plasmas with 18% concentration of 3He), which provides direct and localized electron heating. The plasma scenario is characterized by a reverse magnetic shear configuration, leading to the formation of an electron and ion ITB in the negative shear region. New experimental evidence is gained from the heat wave propagation, which provides new insight into ITB transport physics.