Visual object tracking with RGB and thermal infrared (TIR) spectra available, shorted in RGBT tracking, is a novel and challenging research topic which draws increasing attention nowadays. In this paper, we propose an RGBT tracker which takes spatio-temporal clues into account for robust appearance model learning, and simultaneously, constructs an adaptive fusion sub-network for cross-modal interactions. Unlike most existing RGBT trackers that implement object tracking tasks with only spatial information included, temporal information is further considered in this method. Specifically, different from traditional Siamese trackers, which only obtain one search image during the process of picking up template-search image pairs, an extra search sample adjacent to the original one is selected to predict the temporal transformation, resulting in improved robustness of tracking performance. As for multi-modal tracking, constrained to the limited RGBT datasets, the adaptive fusion sub-network is appended to our method at the decision level to reflect the complementary characteristics contained in two modalities. To design a thermal infrared assisted RGB tracker, the outputs of the classification head from the TIR modality are taken into consideration before the residual connection from the RGB modality. Extensive experimental results on three challenging datasets, i.e., VOT-RGBT2019, GTOT and RGBT210, verify the effectiveness of our method. Code will be shared at https://github.com/Zhangyong-Tang/TAAT.