With the development of liquid-cooled integrated circuits (ICs) using silicon microchannels, the study of heat transfer and thermal modeling in liquid-cooled heat sinks has gained interest in the last five years. As a consequence, several methodologies on the thermally-aware design of liquid-cooled 2-D/3-D ICs and multiprocessor system-on-chips (MPSoCs) have appeared in the literature. A key component in such methodologies is a fast and accurate thermal modeling technique that can be easily interfaced with design optimization tools. Conventional fully numerical techniques, such as finite-element methods, do not render themselves to enable such an easy interfacing with design tools and their order of complexity is too large for fast simulations. In this context, we present a new semi-analytical representation for heat flow in forced convective cooling inside microchannels, which is continuous in 1-D, i.e., along the direction of the coolant flow. This model is based on the well-known analogy between heat conduction and electrical conduction, and introduces distributed electrical parameters in the dimension considered to be continuous, resulting in a state-space representation of the heat transfer problem. Both steady state and transient semi-analytical models are presented. The proposed semi-analytical model is shown to have a closed-form solution for certain cases that are encountered in practical design problems. The accuracy of the model has been validated against state-of-the-art thermal modeling frameworks [1] (errors << 1%), with 3X speed-up of our proposed modeling framework.