The flow and heat transfer performance of Bingham fluid with thermally dependent viscosity across a heated circular tube have been numerically investigated (2408 ≤ ReB ≤ 5852, 9 ≤ Pr ≤ 23 and 10 ≤Bn ≤ 90). The modified bi-viscous Bingham model was used to solve the problem of discontinuous-viscous properties, and a function of temperature known as Arrhenius law was introduced. The results show that unyield regions include a circular shape, pyramid shape, and zones enclosing yield regions at high Reynolds number. Under constant wall temperature boundary, unyield region of temperature-dependent model at rear of circular tube is smaller due to a higher shear rate and lower average viscosity. On the surface of circular tube, local skin drag coefficient first increases and then decreases, and local Nusselt number decreases near rear stagnation point of circular tube illustrating unyield regions of Bingham fluid weaken heat transfer performance. Empirical correlations of average Nusselt number and drag coefficient were obtained based on effects of Reynolds number and Bingham number.