Well integrity monitoring has always been a critical component of subsurface oil and gas operations. Distributed fiber-optic sensing is an emerging technology that shows great promise for monitoring processes, both in boreholes and in other settings. In this study, we present a case study of using distributed temperature sensing (DTS) technology to monitor a cemented and plugged well in the Alaska North Slope (ANS). The well was drilled as part of a long-term gas hydrate study, and the downhole DTS data were recorded over a period of approximately 2 years. By applying a temporal gradient and removing instrument instability noise, we reveal subtle (<0.001°C/h) thermal anomalies, which are characterized by brief warming periods followed by longer cooling periods at discrete depths along the borehole. The observed coherent events show an upward trajectory from deeper formations into the overlying permafrost interval, with the thermal anomalies concentrated in relatively coarse-grained sandstone layers. We also observe that the upward migration rate of the DTS anomalies varies with formation lithology and that there is a spatial and temporal correlation between the subsurface events and measured wellhead annular pressures. We interpret that the observed warming events represent the exothermic process of gas hydrate formation that is occurring in association with the upward migration of gas outside the well casing, and this interpretation is confirmed by numerical simulations. These observations demonstrate the ability of suitably processed DTS data to detect subtle processes and highlight the value of DTS technologies for wellbore integrity monitoring.