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Three dimensional stacked integrated circuits (3D ICs) are extremely attractive for overcoming the barriers in interconnect scaling, offering an opportunity to continue the CMOS performance trends for the next decade. However, from a thermal perspective, vertical integration of high-performance ICs in the form of 3D stacks is highly demanding since the effective areal heat dissipation increases with number of dies (with hotspot heat fluxes up to 250 W/cm2) generating high chip temperatures. In this context, inter-tier integrated microchannel cooling is a promising and scalable solution for high heat flux removal. A robust design of a 3D IC and its subsequent thermal management depend heavily upon accurate modeling of the effects of liquid cooling on the thermal behavior of the IC during the early stages of design. In this paper we present 3D-ICE, a compact transient thermal model (CTTM) for the thermal simulation of 3D ICs with multiple inter-tier microchannel liquid cooling. The proposed model is compatible with existing thermal CAD tools for ICs, and offers significant speed-up (up to 975x) over a typical commercial computational fluid dynamics simulation tool while preserving accuracy (i.e., maximum temperature error of 3.4%). In addition, a thermal simulator has been built based on 3D-ICE, which is capable of running in parallel on multicore architectures, offering further savings in simulation time and demonstrating efficient parallelization of the proposed approach.