Deep transfer learning technology has been successfully applied to the remaining useful life (RUL) prediction of bearings across different working conditions. However, the existing methods encounter the following problems in online scenarios: 1) Due to the drift of online working conditions, it is hard to accumulate the historical data from the same working condition and then build a regression model for the prediction directly. 2) Online target bearing only has the data of the normal state and early fault state, so it is challenging to directly perform transfer learning with the offline bearing data of the fast degradation period. To solve these problems, an online RUL estimation method for unknown working conditions is proposed from the transfer of temporal degradation information. Firstly, a new time series transfer recursive prediction model integrating prior degradation information is constructed. Employing the tensor long short-term memory, the temporal information of the whole-life data in the offline working conditions, such as monotonicity and tendency, is extracted and transferred to the online recursive prediction process for getting online degradation sequence. Then, the transfer component analysis is adopted to adapt the common feature space of the predicted online degradation sequence and existing offline sequences. By extracting domain-invariant features and constructing support vector machine model, the RUL of online bearing can be evaluated. Experiments are conducted on the IEEE PHM Challenge 2012 bearing dataset. The results show that, the proposed method can accurately estimate the degradation trend only using early fault data, and provide an effective solution for the online RUL estimation under an unknown working condition.