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Multispectral pedestrian detection has achieved great success in past years, which can be used in autonomous driving for intelligent transportation system. Most existing multispectral pedestrian detection approaches are developed on the assumption that training and test data belong to an identical distribution, which does not guarantee a good generalization to cross-domain (unseen) data. In this paper, we aim to develop a generalizable multispectral pedestrian detector, which achieves a favorable performance on both intra-dataset evaluation and cross-dataset evaluation. To achieve this goal, we conduct intra-dataset and cross-dataset experiments using single-modal and multi-modal data. By deep analysis, we find that, compared to visible or multi-modal data, thermal data not only has a best cross-dataset generalization, but also generates high-quality proposals on intra-dataset and cross-dataset evaluations. Inspired by this, we propose a novel thermal-first and fusion-second network (called TFNet) for multispectral pedestrian detection. In our TFNet, we first employ a thermal-based proposal network to extract candidate pedestrian proposals. After that, we design a transformer fusion based head network to further classify/regress these proposals. Experiments are performed on three public datasets. The comprehensive results demonstrate the effectiveness of our proposed TFNet on both intra-dataset and cross-dataset evaluations. We hope that our simple design can promote the future study on generalizable multispectral pedestrian detection.