Abstract: Precise temperature monitoring-to the level of a few millikelvin-is essential for the operation of large-scale cryostats requiring a recirculation system. In particular, the performance of Liquid Argon Time Projection Chambers-such as those planned for the DUNE experiment-strongly relies on proper argon purification and mixing, which can be characterized by a sufficiently dense grid of high-precision temperature probes. In this article, we describe the key components of a novel temperature monitoring system developed for a prototype of the DUNE experiment. In particular, a new technique for the cross-calibration of Resistance Temperature Detectors in cryogenic liquids will be presented in detail. This calibration has enabled the validation and optimization of the system's components, achieving an unprecedented relative precision better than 3 mK.