Reasoning over Temporal Knowledge Graphs (TKGs) aims to predict future facts based on the given history. One of the key challenges for prediction is to analyze the evolution process of facts. Most existing works focus on exploring evolutionary information in history to obtain effective temporal embeddings for entities and relations, but they ignore the variation in evolution patterns of facts caused by numerous diverse entities and latent evolving factors, which makes them struggle to adapt to future data with different evolution patterns. Moreover, new entities continue to emerge along with the evolution of facts over time. Since existing models highly rely on historical information to learn embeddings for entities, they perform poorly on such entities with little historical information. To tackle these issues, we propose a novel evolving factor enhanced temporal meta-learner framework for TKG reasoning, MetaTKG++ for brevity. Specifically, we first propose a temporal meta-learner which regards TKG reasoning as many temporal meta-tasks for training. From the training process of each meta-task, the obtained meta-knowledge can guide backbones to adapt to future data exhibiting various evolution patterns and to effectively learn entities with little historical information. Then, we design an Evolving Factor Learning module, which aims to assist backbones in learning evolution patterns by modeling latent evolving factors. Meanwhile, during the training process with the proposed meta-learner, the learnable evolving factor can enhance the meta-knowledge with providing more comprehensive information on learning evolution patterns. Extensive experiments on five widely-used datasets and four backbones demonstrate that our method can greatly improve the performance on TKG prediction.