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Objective. Training deep learning models for image registration or segmentation of dynamic contrast enhanced (DCE) MRI data is challenging. This is mainly due to the wide variations in contrast enhancement within and between patients. To train a model effectively, a large dataset is needed, but acquiring it is expensive and time consuming. Instead, style transfer can be used to generate new images from existing images. In this study, our objective is to develop a style transfer method that incorporates spatio-temporal information to either add or remove contrast enhancement from an existing image. Approach. We propose a temporal image-to-image style transfer network (TIST-Net), consisting of an auto-encoder combined with convolutional long short-term memory networks. This enables disentanglement of the content and style latent spaces of the time series data, using spatio-temporal information to learn and predict key structures. To generate new images, we use deformable and adaptive convolutions which allow fine grained control over the combination of the content and style latent spaces. We evaluate our method, using popular metrics and a previously proposed contrast weighted structural similarity index measure. We also perform a clinical evaluation, where experts are asked to rank images generated by multiple methods. Main Results. Our model achieves state-of-the-art performance on three datasets (kidney, prostate and uterus) achieving an SSIM of 0.91 ± 0.03, 0.73 ± 0.04, 0.88 ± 0.04 respectively when performing style transfer between a non-enhanced image and a contrast-enhanced image. Similarly, SSIM results for style transfer from a contrast-enhanced image to a non-enhanced image were 0.89 ± 0.03, 0.82 ± 0.03, 0.87 ± 0.03. In the clinical evaluation, our method was ranked consistently higher than other approaches. Significance. TIST-Net can be used to generate new DCE-MRI data from existing images. In future, this may improve models for tasks such as image registration or segmentation by allowing small training datasets to be expanded., (Creative Commons Attribution license.)