The effects of the yield number on the steady, incompressible creeping flow of a non-Newtonian Bingham fluid through a four-to-one axisymmetric sudden contraction is studied numerically. The effects of both the yield and Peclet numbers on the thermal field, created due to the viscous dissipation associated with such flows, are investigated. The results demonstrate the dependency of the flow field on the yield number and the strong influence of both the yield and Peeler numbers on the macroscopic and local characteristics of the thermal field. The heat transfer results indicate the significance of beating via viscous dissipation, especially in the vicinity of the contraction plane at high yield numbers.