We investigate the influence of viscous dissipation on the convective heat transfer and entropy generation characteristics for the Poiseuille flow of a viscoelastic fluid in an asymmetrically heated slit microchannel. We use the simplified Phan-Thein-Tanner constitutive equations to describe the rheology of the fluid. Considering hydrodynamic slip at fluid-solid interface, we analytically solve the transport equations to obtain the velocity and temperature fields inside the flow domain, which are further used to evaluate the Nusselt number and the thermodynamic irreversibility generation rate. The results show that the present thermo-fluidic transport process is strongly influenced by the governing dimensionless parameters viz., the Brinkman number, heat flux ratio, viscoelastic group and slip coefficient. Finally, this study reveals that the Brinkman number and viscoelastic parameter have reverse effects on the Nusselt number and entropy generation rate as compared to the slip coefficient. (C) 2018 Elsevier Ltd. All rights reserved.