The grid structure of most numerical thermal simulators has to be designed artificially. Designers might need to try many different grid structures for getting accurate thermal profiles, and, hence, waste a great of runtime. In order to solve this problem, this work presents a system-level thermal simulator, DeNAFE, which can adaptively mesh thermal grids automatically. First, we develop and employ a fast thermal estimation engine to roughly obtain the thermal profile of the system. Then, with this thermal profile, we propose and utilize an adaptive meshing procedure to decide its grid structure and perform thermal simulation. Compared with a commercial tool, ANSYS Icepak, the experimental results show that the speedup of DeNAFE can be up to two orders of magnitude with only 6.09% maximum error for all chips in the steady-state thermal simulation. Furthermore, the error of chips is less than 5.25%, the error of screen/skin is less than 6.03%, and the speedup can be over 171.12 times in the transient simulation.