Heterogeneous temporal graphs (HTGs) are time-evolving graph structures with various nodes and relations. Meta-paths are high-level semantic relationships composed with multiple types of nodes and relations, which can capture the complex semantic information in HTGs. Their semantics can be aggregated from corresponding instances. In HTGs, the aggregation process of historical meta-path instances have significant reference value for the current aggregation. However, previous meta-path aggregation methods could only aggregate information from a single graph, failing to utilize the historical aggregation information. The number and features of meta-path instances vary over time in HTGs, which makes it difficult to find precise references from the aggregation of historical meta-path instances. To solve this problem, we propose the Time-aware Aggregated Meta-path Search (TiAMS) method, which combines the Time-aware Meta-path Aggregation with a meta-path search framework. Specifically, we categorize meta-path instances into several semantic prototypes and establish a semantic coordinate system with them. We map meta-path instances across different timestamps to a unified semantic coordinate system. After that, we capture the potential temporal dependencies in the aggregation of historical instances to guide the current meta-path aggregation. Extensive experiments demonstrate that TiAMS significantly outperforms state-of-the-art baselines for tasks including link prediction, node classification and node regression.