The increasing power density in modern high-performance multi-processor system-on-chip (MPSoC) is fueling a revolution in thermal management. On the one hand, thermal phenomena are becoming a critical concern, making accurate and efficient simulation a necessity. On the other hand, a variety of physically heterogeneous solutions are coming into play: liquid, evaporative, thermoelectric cooling, and more. A new generation of simulators, with unprecedented flexibility, is thus required. In this paper, we present 3D-ICE 3.0, the first thermal simulator to allow for accurate nonlinear descriptions of complex and physically heterogeneous heat dissipation systems, while preserving the efficiency of latest compact modeling frameworks at the silicon die level. 3D-ICE 3.0 allows designers to extend the thermal simulator with new heat sink models while simplifying the time-consuming step of model validation. Support for nonlinear dynamic models is included, for instance to accurately represent variable coolant flows. Our results present validated models of a commercial water heat sink, and an air heat sink plus fan that achieve an average error below 1 degree Celsius and simulate, respectively, up to 3x and 12x faster than the real physical phenomena.