Multi-temporal Point-of-Interest (POI) relationship inference aims to identify evolving relationships among locations over time, providing critical insights for location-based services. While existing studies have made substantial efforts to model relationships with custom-designed graph neural networks, they face the challenge of leveraging POI contextual information characterized by spatial dependencies and temporal dynamics, as well as capturing the heterogeneity of multi-type relationships. To address these challenges, we propose a Triad-Enhanced Spatio-Temporal Network (TESTN), which conceptualizes triads as interactions between relationships for capturing potential interplay. Specifically, TESTN incorporates the spatial 2-hop aggregation layer to capture geographical and semantic information beyond first-order neighbors and the temporal context extractor to integrate relational dynamics within adjacent time segments. Furthermore, we introduce a self-supervised pairwise neighboring relation consistency detection scheme to preserve the heterogeneity of multi-type relationships. Extensive experiments on three real-world datasets demonstrate the superior performance of our TESTN framework.