Application of ion cyclotron resonance heating to the central region of the plasma can produce sawtooth-free periods lasting several confinement times and central electron temperatures in excess of 10 keV. The resulting electron transport is studied locally by examining the relationship between total heat flux and temperature and density gradients. The scatter of data is greatly reduced from that found in a previous study of neutral beam heated discharges; this reduction is due to the absence of sawteeth and the inclusion of radiation profiles, and it improves the accuracy of determining heat diffusivities. The spatial profile of the heat diffusivity is found to be virtually independent of plasma current in the central region and strongly dependent upon current in the outer region. When this result is combined with results obtained from radiofrequency modulation experiments, heat pulse propagation measurements and transient plasma responses from pellet injection, a coherent picture of heat diffusivity profiles emerges. Together, these results confirm that the global confinement time has a dependence upon plasma current which is weaker than linear.