Indoor shortest path query (ISPQ) is of fundamental importance for indoor location-based services (LBS). However, existing ISPQs ignore indoor temporal variations, e.g., the open and close times associated with entities like doors and rooms. In this paper, we define a new type of query called Indoor Temporal-variation aware Shortest Path Query (ITSPQ). It returns the valid shortest path based on the up-to-date indoor topology at the query time. A set of techniques is designed to answer ITSPQ efficiently. We design a graph structure (IT-Graph) that captures indoor temporal variations. To process ITSPQ using IT-Graph, we design two algorithms that check a door's accessibility synchronously and asynchronously, respectively. We experimentally evaluate the proposed techniques using synthetic data. The results show that our methods are efficient.