Networks are difficult to configure correctly, and tricky to debug. These problems are accentuated by temporal and stateful behavior. Static verification, while useful, is ineffectual for detecting behavioral deviations induced by hardware faults, security failures, and so on, so dynamic property monitoring is also valuable. Unfortunately, existing monitoring and runtime verification for networks largely focuses on properties about individual packets (such as connectivity) or requires a digest of all network events be sent to a server, incurring enormous cost. We present a network monitoring system that avoids these problems. Because traces of network events correspond well to temporal logic, we use a subset of Metric First-Order Temporal Logic as the query language. These queries are compiled down to execute completely on the network switches. This vastly reduces network load, improves the precision of queries, and decreases detection latency. We show the practical feasibility of our work by extending a widely-used software switch and deploying it on networks. Our work also suggests improvements to network instruction sets to better support temporal monitoring.