A mathematical model of unsteady non-Newtonian blood flow together with heat transfer through constricted arteries has been developed. The flowing blood is represented as the suspension of all erythrocytes assumed to be Eringen's micropolar fluid and the arterial wall is considered to be rigid having differently shaped stenoses in its lumen arising from various types of abnormal growth or plaque formation. The governing equations of motion accompanied by the appropriate choice of the initial and the boundary conditions are solved numerically by Marker and Cell (MAC) method and the results are checked for numerical stability with desired degree of accuracy. The quantitative analysis carried out finally includes the respective profiles of the flow-field and the temperature distribution over the entire arterial segment as well. The key factors like the wall shear stress, the stream lines, the separation-reattachment points, the pressure drop and the heat contours are also examined for further qualitative insight into the heat flow phenomena. Results show that the initiation of nonzero microspin velocity on the arterial wall prompts early flow separation and the occurrence of multiple separation zones may also be attributed due to the introduction of nonzero microspin boundary condition parameter S together with the rough valleys and ridges presented on the outline of the diverging part of the irregular stenosis. The present results also predict the excess pressure drop across the cosine stenoses than the irregular ones and show quite consistency with several existing results in the literature which substantiate sufficiently to validate the applicability of the model under consideration. (C) 2012 Elsevier Ltd. All rights reserved.