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Recent developments in acquisition techniques are resulting in a very rapid growth of the number of available three dimensional (3D) models across areas as diverse as engineering, medicine and biology. It is therefore of great interest to develop the efficient shape retrieval engines that, given a query object, return similar 3D objects. The performance of a shape retrieval engine is ultimately determined by the quality and characteristics of the shape descriptor used for shape representation. In this paper, we develop a novel shape descriptor, called temperature distribution (TD) descriptor, which is capable of exploring the intrinsic geometric features on the shape. It intuitively interprets the shape in an isometrically-invariant, shape-aware, noise and small topological changes insensitive way. TD descriptor is driven by by heat kernel. The TD descriptor understands the shape by evaluating the surface temperature distribution evolution with time after applying unit heat at each vertex. The TD descriptor is represented in a concise form of a one dimensional (1D) histogram, and captures enough information to robustly handle the shape matching and retrieval process. Experimental results demonstrate the effectiveness of TD descriptor within applications of 3D shape matching and searching for the models at different poses and various noise levels.