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Based on the conception of the cyclic (wave) nature of the changes in the circulation of the atmosphere of the Atlantic-European sector (index of the North Atlantic oscillations) and surface temperature of the Black Sea on scales smaller or equal to the century scale, anomalies of the winter surface temperature are analyzed. It is shown that in the phase of the maximum of the presumably 60-year cycle of changes in the NAO index a negative anomaly of surface temperature forms and in the phase of minimum of this scale of changes of NAO, there is a positive anomaly. Estimates of the possible thermal state of the surface of the Black Sea during the phase of the expected minimum in 2011-2020 of the 60-year cycle (60-year wave) of the NAO index are made. The possibility of a phase shift between changes in solar activity, the NAO index, and anomalies of temperature of the Black Sea on the scales of cyclic (wave) processes larger than 100 years is considered. [ABSTRACT FROM AUTHOR]