Temporal data naturally arise in various emerging applications, such as sensor networks, human mobility or internet of things. Clustering is an important task, usually applied a priori to pattern analysis tasks, for summarization, group and prototype extraction; it is all the more crucial for dimensionality reduction in a big data context. Clustering temporal data under time warp measures is challenging because it requires aligning multiple temporal data simultaneously. To circumvent this problem, costly k-medoids and kernel k-means algorithms are generally used. This work investigates a different approach to temporal data clustering through weighted and kernel time warp measures and a tractable and fast estimation of the representative of the clusters that captures both global and local temporal features. A wide range of 20 public and challenging datasets, encompassing images, traces and ecg data that are non-isotropic (i.e., non-spherical), not well-isolated and linearly non-separable, is used to evaluate the efficiency of the proposed temporal data clustering. The results of this comparison illustrate the benefits of the method proposed, which outperforms the baselines on all datasets. A deep analysis is conducted to study the impact of the data specifications on the effectiveness of the studied clustering methods.