Double transport barrier modes (simultaneous core and edge transport barrier) have been observed with off-axis ion cyclotron range of frequencies (ICRF) heating in the Alcator C-Mod tokamak [I.H. Hutchinson et al., Phys. Plasmas 1, 1511(1994)]. An internal transport barrier (ITB) is routinely produced in enhanced D[alpha] H-mode (EDA) discharges where the minority ion cyclotron resonance layer is at r/a (0.5) during the current flat top phase of the discharge. The density profile becomes peaked without the presence of a particle source in the plasma core and continues to peak until the increased core impurity radiation arrests the improved energy confinement, ultimately leading to a barrier collapse. With the addition of moderate (0.6 MW) central ICRF heating, the double barrier mode was maintained for as long as the ICRF power was applied and modeling shows that the internal thermal barrier was maintained throughout the discharge. The presence of sawteeth throughout most of the ITB discharge allows sawtooth induced heat pulse analysis to be performed. This analysis indicates that there is an abrupt radial discontinuity in the heat pulse time to peak profile when an ITB is present. Furthermore, this discontinuity appears to move into the core plasma from the edge region in about 0.2 sec, several confinement times. The deduced thermal diffusivity, Xhp indicates a barrier exists in the electron thermal transport, the barrier is limited to a narrow radial region, and the transport is unaffected outside this narrow radial extent.