IoT networks in, for example, smart manufacturing, smart homes, and smart health demand process mining beyond traditional event logs. However, conventional process discovery and conformance checking algorithms expect data to be collected at a central location for mining. As a result, they struggle to handle the vast amounts of data generated by IoT networks, which often leads to privacy concerns. To address these challenges, this paper introduces Distributed Conformance Checking (DisCC). DisCC leverages a footprint-fitness method to perform distributed online conformance checks directly at the data source where an event is sensed, ensuring scalable conformance checking and enabling privacy by only sharing aggregated event data with a central entity. Our evaluation of DisCC demonstrates its effectiveness in accurately performing conformance checks at the event, trace, and log levels. We experimentally show the correctness of DisCC and how quickly its interim results converge to the correct fitness value. The system supports real-time alerts for non-conforming events and traces, detects concept drifts and temporary fitness losses through a sliding window implementation, and offers a scalable, privacy-enabling solution for process monitoring in IoT networks.