Micro/nano-ring or ring-based resonators are popular core components of sensors and actuators. Accurately predicting the quality factor (Q) based on thermoelastic damping (TED) is intensively crucial for designing high-performance micro/nano-ring resonators. In this work, adopting the modified-couple-stress (MCS) and nonlocal-dual-phase-lagging (NDPL) models, analytical TED expressions are developed for circular cross-section micro/nano-rings undergoing out-of-plane vibration for the first time. Multiple effects are considered in the modeling procedure, which are size-dependence effects in the mechanical and thermal fields, the non-Fourier effect of heat conduction, and three-dimensional temperature gradients in the circumferential, radial, and tangential directions. Therefore, the proposed TED models are more comprehensive compared to existing TED models. The coefficients (CC and CM) associated with the out-of-plane vibration mode are examined from an energy-ratio perspective. Moreover, the investigation is focused on the impacts of the MCS and NDPL non-Fourier effects on the fluctuation temperature and TED spectra. The results indicate as CC and CM approach one, the bending energy emerges as the predominant component of the stored energy. Notably, the NDPL non-Fourier effect significantly affects the fluctuation temperature within the ring operated in high-order modes. In special, the distributions of fluctuation temperature in the circumferential direction exhibit periodic patterns that are closely correlated with the modal order. Furthermore, TED can be suppressed by the MCS size-dependence effect. Meanwhile, the behavior of TED at high frequencies is simultaneously determined by the dimension of heat conduction, phase-lagging times, and nonlocal thermal-length parameter.