Extensive results elucidating the effect of severe blockage on drag coefficient and Nusselt number for a heated sphere sedimenting in Bingham plastic fluids on the axis of a long cylindrical tube over wide ranges of blockage ratio (0.5 <=lambda <= 0.95), Reynolds number (1 <= Re <= 100), Prandtl number (5 <= Pr <= 100) and Bingham number (0.01 <= Bn <= 100) are reported in this study. Both drag coefficient and Nusselt number are enhanced with the increasing values of lambda and Bn due to the sharpening of the velocity and temperature gradients on the surface of the sphere and the backflow of the fluid displaced by the falling sphere along with the diminishing yielded regions. The influence of velocity distribution in the tube also gradually weakens with the increasing lambda and Bn. However, the constant heat flux condition prescribed on the surface of the sphere is more effective in promoting heat transfer than the case of an isothermal sphere. The regions of fluid-yielding expand with the increasing Reynolds number which is countered by the increasing Bingham number. The present numerical results have been consolidated via simple correlating expressions with acceptable levels of accuracy.