The present-day climate (the recent 100–150 years) obviously constitutes the structure of a global intra-system rhythmic process with an individual rhythm of about 60 years. In turn, each of the rhythms is presented by the two climate phases of about 25–35 years characterized by qualitative differences: one phase is relatively continental, while the other is humid. Globality and quasi-synchronism of environmental changes are accompanied by planetary structures: the Global Atmospheric Oscillation (GAO) in the atmosphere and the Multidecadal Oscillation of the Heat content in the Ocean (MOHO) discovered relatively recently. Unexpected and rapid qualitative phase changes in the climate, which first focused attention in the mid-1970s of the last century, were titled “climate shifts”. The revealed features of the present-day climate are of exceptional scientific and practical interest and deserve the development of methods for predicting the timing of the forthcoming climate shift. Arising unexpectedly and accompanied by rapid significant changes, these shifts identified the problem of understanding the nature and establishing the processes and mechanisms causing them. First of all, of interest are phase changes in the thermodynamic state of the climate system components: the ocean, atmosphere, and continents. As a result of the World Ocean (WO) thermohydrodynamics numerical modelling, it is shown that MOHO is localized in the layer of the main thermocline, where the most important elements of the WO circulation are located. The performed study based on observational data allows us to conclude that, during the phase of the WO thermal discharge (1975–1999), the two key systems of currents, the Kuroshio and the Gulf Stream, were under similar thermodynamic conditions.