In this work, we present milliTRACE-IR, a joint mm-wave radar and infrared imaging sensing system performing unobtrusive and privacy preserving human body temperature screening and contact tracing in indoor spaces. Social distancing and fever detection have been widely employed to counteract the COVID-19 pandemic, sparking great interest from academia, industry and public administrations worldwide. While most solutions have dealt with the two aspects separately, milliTRACE-IR combines, via a robust sensor fusion approach, mm-wave radars and infrared thermal cameras. The system achieves fully automated measurement of distancing and body temperature, by jointly tracking the faces of the subjects in the thermal camera image plane and the human motion in the radar reference system. It achieves decimeter-level accuracy in distance estimation, inter-personal distance estimation (effective for subjects getting as close as 0.2 m), and accurate temperature monitoring (max. errors of 0.5 C). Moreover, milliTRACE-IR performs contact tracing: a person with high body temperature is reliably detected by the thermal camera sensor and subsequently traced across a large indoor area in a non-invasive way by the radars. When entering a new room, this subject is re-identified among several other individuals with high accuracy (95%), by computing gait-related features from the radar reflections through a deep neural network and using a weighted extreme learning machine as the final re-identification tool.