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This paper presents a new algorithm to efficiently maintain Bounding-Volume Hierarchies (BVHs) for fast distance queries with deformable polygon meshes using multi-core architectures. The method involves inflating the bounding volumes in an efficient manner to guarantee the enclosure of the deformable model within the BVH at all times. This is done at low additional computation and memory cost without significantly degrading the quality of the BVH and also in a fashion that allows a simple parallel implementation. Additionally, to facilitate fast queries specifically for deforming meshes, we propose a novel algorithm for the bottom-up construction of BVHs that results in much faster distance queries.