A heating source with off-axis electron cyclotron heating (ECH) alone produced a plasma with a quasi-steady-state hollow electron-temperature profile in the Large Helical Device. The clear formation of this quasi-steady-state hollow electron-temperature profile can be explained by adding the outward heat convection term to the diffusion term, as a simple model to describe the electron heat flux, using the energy conservation equation. In addition, we directly observed the non-locality of the non-diffusive (convective) contribution in transient electron thermal transport in the condition that power-modulated on-axis ECH was applied to the plasma sustained by off-axis ECH. The experimentally evaluated flux-gradient relation shows two different positive values of the electron heat flux at zero temperature gradient by going back and forth between positive and negative temperature gradient regions in the transport hysteresis phenomenon.