This paper presents the design and implementation of TAPOR, a privacy-preserving, non-contact, and fully passive sensing system for accurate and robust 3D hand pose reconstruction for around-device interaction using a single low-cost thermal array sensor. Thermal sensing using inexpensive and miniature thermal arrays emerges with an excellent utility-privacy balance, offering an imaging resolution significantly lower than cameras but far superior to RF signals like radar or WiFi. The design of TAPOR, however, is challenging, mainly because the captured temperature maps are low-resolution and textureless. To overcome the challenges, we investigate thermo-depth and thermo-pose properties, proposing a novel physics-inspired neural network that learns effective 3D spatial representations of potential hand poses. We then formulate the 3D pose reconstruction problem as a distinct retrieval task, enabling accurate hand pose determination from the input temperature map. To deploy TAPOR on IoT devices, we introduce an effective heterogeneous knowledge distillation method, reducing computation by 377x. TAPOR is fully implemented and tested in real-world scenarios, showing remarkable performance, supported by four gesture control and finger tracking case studies. We envision TAPOR to be a ubiquitous interface for around-device control and have open-sourced it at https://github.com/aiot-lab/TAPOR.