There is inadequate work done on tapered and stenois blood vessel under thermotheraphy, experimental studies being impossible to be conducted since the system is unlike mechanical system which could be modeled in the lab. In this study, the blood flow and heat transfer in an artery under various heating conditions have been numerically simulated. Three different cases of blood vessels are considered: straight vessel, converging tapered vessel and stenois vessel. Constant heat flux was applied at several intensities in each case. It was shown that the flow simulated at the vena contracta is analogous to the flow in a converging-diverging nozzle. However, the dimensionless center velocity at outlet region was found to be higher than that at the inlet region which could be due to the slow recovery of pressure after the stenois region. The local Nusselt number fluctuated at both the downstream and upstream which could have been caused by recirculation as the flow entered and exit the stenois region. Results in general have shown that blood flow in biological systems may well behave like the mechanical systems.