As the economic value of cryptocurrencies continues to ascend, an increasing number of cybercriminals exploit malicious browser scripts to commandeer the system and network resources of victims for unauthorized cryptocurrency mining. This form of browser-based mining, termed crypto-jacking, imparts substantial impact and harm to society, enterprises, and users. However, existing research methods lead to poor transferability because they require model training using labeling data from detection devices. To solve this problem, we introduce a crypto-jacking detection method based on time series representation learning, called TSR-jack. Specifically, we first collect hardware runtime system data for a period of time and generate datasets. After slicing the time series datasets, they are used to train a time series representation model, which introduces the loss of temporal information to extract temporal features. The temporal features can capture similarities between different devices and therefore address model transfer difficulties. Finally, the time vectors obtained from representation learning are fed into SVM for classification. Experimental results show that our TSR-jack method outperforms similar dynamic feature detection methods, especially when considering transferability, with a precision improvement of more than 5%.