We address the problem of enumerating all temporal k-cores given a query time range and a temporal graph, which suffers from poor efficiency and scalability in the state-of-the-art solution. Motivated by an existing concept called core times, we propose a novel algorithm to compute all temporal $k$-cores based on core times and prove that the algorithmic running time is bounded by the size of all resulting temporal k-cores, which is optimal in this scenario. Meanwhile, we show that the cost of computing core times is much lower, which demonstrates the close relevance between our overall running time and the result size.