Diffuse myocardial diseases can be diagnosed using T1 mapping technique based on T1 relaxation times from MRI data. The T1 relaxation parameter is acquired through pixel-wise fitting of the MRI signal. Hence, pixels misalignment resulted by cardiac motion leads to an inaccurate T1-mapping. Therefore, registration is needed. However, due to the intensity differences between the different time-points, recent unsupervised deep-learning approaches based on minimizing the mean-squared-error (MSE) between the images cannot be utilized directly. To overcome this challenge, we propose a new double-stage method, in which a style-transfer is used to harmonize the signal intensities over time, followed by an unsupervised deep-learning based minimization of the MSE between the images. We evaluated our approach on a publicly available cardiac T1 mapping database of 210 subjects. Our approach achieved the best median model-fitting R^2 compared to baseline methods (0.9794, vs. 0.9651/0.9744/0.9756) and T1 values which are much closer to the the expected myocardial T1 value. Furthermore, both metrics have less variability compared to the other methods.