This work presents an adaptive thermal grid generation method, MErBAG, in the system-level thermal simulation. Firstly, MErBAG iteratively evaluates the grid quality locally by analyzing thermal resistances and temperatures of target grids. Then, MErBAG introduces and utilizes two metrics, non-linearization degree and junction error, to adaptively mesh grids. Finally, we integrate MErBAG into an iterative method for solving linear equations to perform thermal simulation. Compared with an existing machine learning based meshing method, the experimental results show that MErBAG can provide better quality adaptive thermal meshes but use less number of thermal grids.