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Almost three-quarters of known volcanic activity on Earth occurs in underwater locations. The presence of active hydrothermal vent fields in such environments is a potential natural hazard for the environment, society, and economy. Despite its importance for risk assessment and risk mitigation, the monitoring of volcanic activity is impeded by the remoteness and the extreme conditions of many underwater volcanoes. The morphology and the activity of the submarine caldera, Avyssos, at the northern part of Nisyros volcano in the South Aegean Sea (Greece), were studied using a remotely operated underwater vehicle. The recorded time series of temperature and conductivity over the submarine volcano have been analyzed in terms of the Generalized Moments Method. This type of analysis can be used as an indicator for the state of activity of a submarine volcano. Here, we expand the work conducted for the first time in 2018. We present the findings of the geological exploration and the mathematical analysis, obtained from the data collected in October 2010. The temperature and conductivity time series show minor fluctuations in a rather stable environment. Based on these results, the impact of developing appropriate mechanisms and policies to avoid the associated natural hazard is expected to be important.