Two-phase liquid cooling of computer chips via microchannels etched directly on silicon dies is a potential long-term solution to enable continued integration of high-performance multiprocessors. Two-phase cooling refers to the heat removal via evaporation of a refrigerant flowing inside a heat sink. While possessing superior cooling properties, large-scale use of this technology in the industry is limited by the lack of thermal modeling tools that can accurately predict temperatures in a two-phase cooled IC. In this paper, we propose STEAM, a new compact thermal model for 2D/3D ICs with two-phase cooling via silicon microchannels. The accuracy of the STEAM model is validated against measurements from a real two-phase cooled IC test stack reported previously in literature. Temperatures were predicted with an average error as low as 10.2% for uniform heat fluxes and 6.9% for hotspots. Finally, the STEAM model is applied to a realistic 3D multiprocessor system-on-chip (3D MP-SoC) with two-phase cooling to simulate IC temperatures and the refrigerant pumping power, demonstrating the applicability of STEAM in the early-stage design of near-future high-performance computers with two-phase cooling.