A parametric investigation is carried out on the effects of temperature-dependent viscosity and viscous dissipation in simultaneously developing laminar flows of liquids in straight microchannels of constant cross sections. Reference is made to fluid heating conditions with a uniform heat flux imposed on the walls of the microchannels. Six different cross sectional geometries are considered, chosen among those usually adopted for microchannels (circular, flat, square, rectangular, trapezoidal, and hexagonal). Viscosity is assumed to vary with temperature according to an exponential relation, while the other fluid properties are held constant. A finite-element procedure is employed for the solution of the parabolized momentum and energy equations. Due to the high value of the ratio between the length and the hydraulic diameter in microchannels, such an approach is very advantageous with respect to the one based on the steady-state solution of the elliptic form of the governing equations in a three-dimensional domain corresponding to the whole microchannel. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented. Numerical results confirm that, in the laminar forced convection in the entrance region of straight microchannels, the effects of temperature-dependent viscosity and viscous dissipation cannot be neglected in a wide range of operative conditions.