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While vision transformers (ViTs) have continuously achieved new milestones in the field of computer vision, their sophisticated network architectures with high computation and memory costs have impeded their deployment on resource-limited edge devices. In this paper, we propose a hardware-efficient image-adaptive token pruning framework called HeatViT for efficient yet accurate ViT acceleration on embedded FPGAs. By analyzing the inherent computational patterns in ViTs, we first design an effective attention-based multi-head token selector, which can be progressively inserted before transformer blocks to dynamically identify and consolidate the non-informative tokens from input images. Moreover, we implement the token selector on hardware by adding miniature control logic to heavily reuse existing hardware components built for the backbone ViT. To improve the hardware efficiency, we further employ 8-bit fixed-point quantization, and propose polynomial approximations with regularization effect on quantization error for the frequently used nonlinear functions in ViTs. Finally, we propose a latency-aware multi-stage training strategy to determine the transformer blocks for inserting token selectors and optimize the desired (average) pruning rates for inserted token selectors, in order to improve both the model accuracy and inference latency on hardware. Compared to existing ViT pruning studies, under the similar computation cost, HeatViT can achieve 0.7%$\sim$8.9% higher accuracy; while under the similar model accuracy, HeatViT can achieve more than 28.4%$\sim$65.3% computation reduction, for various widely used ViTs, including DeiT-T, DeiT-S, DeiT-B, LV-ViT-S, and LV-ViT-M, on the ImageNet dataset. Compared to the baseline hardware accelerator, our implementations of HeatViT on the Xilinx ZCU102 FPGA achieve 3.46$\times$$\sim$4.89$\times$ speedup.