In this paper we present a giant-area fiber-optic gyroscope (GAFOG) combining a Raman distributed temperature sensor (RDTS) for metrological monitoring of Earth rotation rate fluctuations. The GAFOG exhibits sensitivity limits in Earth rotation sensing associated to temperature variations along the fiber. Distributed temperature measurements providing an accurate fiber temperature mapping, enable tracking of the signal phase drifts. This allows reduction of the phase noise at low Fourier frequencies, and a corresponding enhancement of the Earth rotation rate variation sensitivity beyond the currently achieved 2•nrad/s for integration times of 1000 s.