Nusselt number has unique characteristics under uniform wall temperature (UWT) and uniform wall heat flux (UWHF) thermal boundary conditions in twisted elliptical tube. Twisting of elliptical tube produces larger local Nusselt number under UWT than that under UWHF in some regions. In order to discover the mechanisms to form such characteristics in twisted elliptical tube, the velocity contribution and velocity gradient contribution to the transport of the heat flux defined by Fourier's law, q, are numerically investigated in this paper. Velocity gradient under UWHF contributes more greatly to the transport of the heat flux under UWHF than under UWT, which results larger local Nusselt number under UWHF than under UWT in straight elliptical tube. Velocity and its gradient contributions to the transport of the heat flux nearly normal to the wall surface have larger values under UWHF than under UWT in most regions, which produces larger local Nusselt number in twisted elliptical tube under UWHF than under UWT in these regions. In some regions velocity and its gradient contributions to the transport of the heat flux nearly normal to the wall surface have larger values under UWT than under UWHF produces larger local Nusselt number in twisted elliptical tube under UWT than under UWHF in these regions.