Melt flow in extrusion dies and the metering zone of extrusion screws is in general modeled as a steady state flow. This means that the velocity profile and pressure build-up in the metering zone is fully developed as well as the temperature of the cylinder and cylinder wall are in thermal equilibrium. Due to the fact that the dosing phase in rubber injection molding is a start-up process transient boundary conditions must be used for the mathematical description of the material-temperature. In this work, we calculated the material-temperature using a two-dimensional rectangular channel neglecting the edge and wall influences instead of a three-dimensional screw-channel. Firstly, the equation of momentum will be solved using the power law for the flow in and perpendicular to the channel. Secondly, for an infinitesimal volume element the energy balance equation including shear dissipation and heat conduction was formulated. This leads to an inhomogeneous first order differential equation with variable coefficients, which must be solved for each infinitesimal volume element as well as for each time step. The time step reflects the transient state of the boundary conditions which were determined experimentally. For the determination of the transient boundary conditions a specially designed screw test stand consisting of a plasticizing cylinder and a downstream throttle valve was used. The layout of the plasticizing cylinder and the temperature control is identical to a vertical Maplan rubber injection molding machine, but additionally the screw test stand is equipped with pressure and temperature sensors to monitor the boundary conditions. Furthermore, the throttle valve offers the ability to measure the temperature distribution of the dosed material. It could be shown that the temperature build-up during the transient dosing process can be modeled with an error of about 5% in relation to the experimentally determined material-temperature.