The thermal characteristics of Bingham plastic fluid flows are analyzed in circular microchannels under uniform wall heat flux condition. The analytic approach presented here reveals that the governing parameters are Bingham number, dimensionless radius of the plug flow region, and Brinkman number. The results demonstrate that there is a strong influence of viscous dissipation on heat transfer and entropy generation for Brinkman numbers greater than a specific value. With increasing the Brinkman number and dimensionless radius of the plug flow region, entropy generation is increased, while the Nusselt number is decreased. The influence of these parameters on the entropy generation from heat transfer is strongly higher than the entropy generation from fluid friction. The average dimensionless total entropy shows that the Bingham plastic fluids generate entropy more than Newtonian fluids; also, an increase in the dimensionless radius of the plug flow region results in increasing the average dimensionless total entropy generation. By letting the dimensionless radius of the plug flow region equal to zero, the generalized expressions and results will be simplified to Newtonian fluids.