Battery management system (BMS) is crucial to ensure the efficiency and safety of the Lithium-ion battery pack by monitoring the real-time voltage, current, and temperature. In particular, the monitoring and warning system of the BMS is especially vital and demanding. However, most researchers separate the battery states as individual tasks and discuss them respectively, while state of charge (SOC), state of health (SOH), and state of temperature (SOT) are coupled and should be estimated simultaneously in one model. To satisfy the demand for the online monitoring and warning system, this paper proposed an integrated estimation model based on temporal convolution network (TCN) and multi-task learning taking the mutuality of the SOC, SOH and SOT into consideration. Specifically, four assessing indexes were obtained by analyzing the relationship, tendency and characteristic of the temperature and capacity during the battery aging process. Then, a multi-timescale model was built combined with the conception of multi-task learning, namely the hierarchical temporal convolutional network (HTCN), and the temperature varying tendency is predicted along with the battery states as different output tasks. At last, the model was transferred to test datasets to validate the generality, accuracy and robustness. Results show that the mean average error (MAE) of the SOC, SOH and SOT estimation are 1.37%, 0.95% and 1.01%, respectively. This paper provided a novel, practical and reliable route for the comprehensive BMS construction.