Tracking　a　suspicious　car　or　a　person　in　a　city　efficiently　is　crucial　in　urban　safety　management.　But　how　can　we　complete　the　task　with　the　minimal　number　of　spatiotemporal　searches　when　massive　camera　records　are　involved?　To　this　end,　this　study　proposes　a　strategy　named　intermediate　searching　at　heuristic　moments　(IHMs).　At　each　step,　we　determine　which　moment　is　the　best　one　for　the　search　based　on　a　heuristic　indicator.　Then,　at　that　moment,　locations　are　searched　one　by　one　in　descending　order　of　predicted　appearing　probabilities　until　a　search　hit　is　obtained.　We　iterate　this　step　until　we　derive　the　object＇s　current　location.　Five　searching　strategies　are　compared　via　experiments.　Among　these　strategies,　the　IHMs　strategy　is　validated　as　the　most　efficient.　IHMs　can　save　up　to　1/3　of　the　total　cost.　This　result　provides　evidence　that　＂searching　at　intermediate　moments　can　save　cost.＂