The edge-localized, high-confinement mode regime is of interest for future Tokamak reactors since high performance has been sustained for long durations. Experiments in the Joint European Tokamak [M. Keilhacker et al. , Nuclear Fusion 39 , 209 (1999)] have studied this regime using scans with the toroidal field and plasma current varied together in H, D, DT, and T isotopes. The local energy transport in more than fifty of these plasmas is analyzed, and empirical scaling relations are derived for energy transport coefficients during quasi-steady state conditions using dimensionless parameters. Neither the Bohm nor gyro-Bohm expressions give the shapes of the profiles. The scalings with b and n * are in qualitative agreement with Ion Temperature Gradient theory.