This research focuses on numerical patterns of temperature distribution and blood flow through tapered arteries. The blood flow is considered as an incompressible and fully developed flow with Non-Newtonian nature assumed as modified Cross fluid which is inside a body under certain acceleration. Also, the impact of heat transfer regarding a single layer model on an unstable and pulsatile blood flow through a designed tapered artery with a combination of stenotic and aneurysm is investigated. The wall of artery is designed as an elastic tube, so, its geometry changes during the numerical computations is up to time. This research uses a suitable coordinate transformation to create an exact mesh with rectangular mesh units. In the case of the thermophysical parameters of blood flow field including the velocity pattern and temperature distributions, the governing equations are managed and solved based on the finite difference method and then, the reported results are discussed as a function of velocity and temperature. The outputs of this mathematical modeling are compared with some available and proved results in previous researches to confirm the accuracy and validity of the method. The variations in dynamic features of blood flow wall shear stress, volumetric flow rate and flow resistance can be analyzed and computed on basis of the pattern of velocity profile in assumed domain. Furthermore, contour plots of temperature and velocity for specified parameters are provided.