We discuss the issues of primary importance to understand the nature of climate changes in the 20th century and main physical processes responsible for these changes and present a physical model for the solar activity (SA) effect on climate characteristics. A key concept of this model is the heliogeophysical disturbance effect on the Earth climate system parameters driving the long-wave radiation flux moving away from the Earth out into space in high-latitude regions. We address the solar activity effect on the changes in the temperature of the atmosphere and of the World Ocean. The aa–index of the geomagnetic activity (GA) was used as an SA proxy index. We discuss the results of analyzing the regularities and peculiarities of the tropospheric and sea surface temperature (SST) responses to both separate heliogeophysical disturbances and long-term changes in solar and geomagnetic activity. The structure of the tropospheric and SST temperature responses was shown to feature a spatial time irregularity. We revealed the regions, where long-term SST changes are determined mainly by SA variations.