Multi-spectral template matching (MSTM) based object detection approaches can be widely used in robotics and aerospace systems for fine-grained object discovery. However, the performance of existing nearest neighbor search based nonparametric paradigms (e.g., correlation coefficient and lp-norm) turns out to be unsatisfactory. These paradigms tend to suffer from two defects: 1) they fail to select from the raw features the discriminative ones that can help distinguish between the target and background; 2) the domain shift between the template and search spectra has not been well addressed within the feature space. In this work, we propose a data-driven MSTM method to address these two issues. First, Exemplar-SVM (E-SVM) is applied to execute feature selection and target/background categorization jointly, which is facilitated by its max-margin mechanism. To enable the learning process where the template is regarded as a single positive sample, knowledge transfer is executed to attain negative samples from other domains, e.g., large-scale public datasets. Then, the hard negative samples are mined to help train a discriminative classifier. Concerning practical applications, we also augment the template with different image degradations and extend E-SVM from the original one-shot learning approach to its few-shot version. Second, a multi-domain adaptation approach via unsupervised multi-domain subspace alignment is proposed to tackle multi-domain shift problem. Here the multiple domains relate to template, search, and negative ones considering both offline learning and online matching. The wide-range experimental results on two multi-spectral datasets demonstrate the effectiveness of our method. The tailored dataset and code will be released publicly.