Battery health prognostic is a key part of battery management used to ensure safe and optimal usage. A novel method for end-to-end sensor-free differential temperature voltammetry reconstruction and state of health estimation based on the multi-domain adaptation is proposed in this paper. Firstly, the partial charging or discharging curve is used to reconstruct the differential temperature curve, removing the requirement for the temperature sensor measurement. The partial differential capacity curve and the reconstructed differential temperature curve are input and then used in an end-to-end state of health estimation. Finally, to reduce the domain discrepancy between the source and target domains, the maximum mean discrepancy is included as an additional loss to improve the accuracy of both differential temperature curve reconstruction and state of health estimation with unlabeled data from the testing battery. Four data sets containing both experimental data and public data with different battery chemistry and formats, current modes and rates, and external conditions are used for the verification and evaluation. Experimental results indicate the proposed method can satisfy health prognostics under different scenarios with mean errors of less than 0.067 degrees C/V for differential temperature curves and 1.78% for the state of health. The results show that the error for the differential temperature curve reconstruction is reduced by more than 20% and the error for the state of health estimation is reduced by more than 47% of the proposed method compared to the conventional data-driven method without transfer learning.