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This paper presents NanoHeat, a multi-resolution full-chip dynamic integrated circuit (IC) thermal analysis solution, that is accurate down to the scale of individual gates and transistors. NanoHeat unifies nanoscale and macroscale dynamic thermal physics models, for accurate characterization of heat transport from the gate and transistor level up to the chip-package level. A non-homogeneous Arnoldi-based analysis method is proposed for accurate and fast dynamic thermal analysis through a unified adaptive spatial-temporal refinement process. NanoHeat is capable of covering the complete spatial and temporal modeling spectrum of IC thermal analysis. The accuracy and efficiency of NanoHeat are evaluated, and NanoHeat has been applied to a large industry design. The importance of considering fine-grain temperature information is illustrated by using NanoHeat to estimate temperature-dependent negative-bias-temperature-instability (NBTI) effects. NanoHeat has been implemented and publicly released for free academic and personal use.