We are developing the Temperature Monitoring System for DUNE far detectors. For the first module, the electric field prevents the usage of RTDs inside the active volume of the Time Projection Chamber. Fiber Bragg Grating (FBG) constitutes an emerging technology, which have been well studied and used to monitor strain and temperature in engineering structures at ambient temperatures. However, insufficient R&D exists in cryogenic environments and the precision required for our application (< 0.005º) has not yet been achieved. IFIC is leading the R&D on this technology for its usage to monitor liquid argon temperatures in DUNE.