Photonic integrated resonators have advantages over traditional benchtop cavities in terms of size, weight, and cost with the potential to enable applications that require spectrally pure light. However, integrated resonators suffer from temperature-dependent frequency variations and are sensitive to external environmental perturbations, which hinders their usage in precision frequency applications. One solution is to use interrogation of the cavity temperature through dual-mode optical thermometry (DMOT) by measuring the shift of the resonance frequency difference between two polarization or optical frequency modes. Yet this approach has only been demonstrated in bulk-optic whispering gallery mode and fiber resonators. In this paper, we implement dual-mode optical thermometry in an ultra-high Q integrated silicon nitride resonator for the first time, to the best of our knowledge. A dual-mode resonance frequency difference temperature sensitivity of 188 ± 15 MHz/K is measured. We demonstrate feedforward DMOT frequency correction that, under an applied external temperature ramp, is able to reduce the optical frequency change to 0.31 kHz/s as compared to an uncorrected 10.03 kHz/s, a factor of 30X reduction. These results show promise for on-chip frequency correction solutions for quantum, metrology, atomic and coherent optical communications applications.