Energy transport by the electrons in a tokamak is examined in steady-state and power modulation experiments using electron cyclotron heating. The results are consistent with the assumption that temperature profiles are limited by a critical gradient length, leading to "stiff" profiles. The modulation experiments show that the stiffness factor increases with temperature. They strongly suggest that turbulence driven by the electron temperature gradient may be a dominant mechanism of electron transport. Although possibly not universal, these results are valid under various plasma conditions.