The main interactions of the Total Solar Irradiance (TSI) variations with the climatic system are considered. This research introduced new physically based indexes for 11-year cycles: the integral relative energetic power of the cycles solar activity (SA) and TSI, as well as the cycle-weighted mean value both of the TSI and sunspot number. The observed cycle-average TSI value in cycles XXII–XXIV has decreased by more than 0.5 W/m2, indicating its quasi-bicentennial decline. The onset of the Maunder-type Grand minimum phase of the SA and TSI of the quasi-bicentennial cycle (BCC) is expected in the 27th or 28th 11-year cycle in 2042 or 2053. The Earth's thermal inertia will cause a temperature reduction of around 0.25 K due to the deficit in TSI during the declining phase of the bicentennial cycle due to its negative impact on Earth's energy imbalance. As a result, the Bond's albedo will increase, and the abundance of atmospheric water vapor and carbon dioxide will decrease as a response to a direct solar forcing. BCC feedback mechanisms will also continue operating during both its minimum and maximum phases. The feedback mechanisms will continue further in short periods (about 30 years) at the beginning of BCC's growth and decline phases. These long-term self-reinforcing feedback effects will act as a response to the TSI, forcing in such a way as to trigger a strong amplification of the initial direct input to the corresponding temperature changes. They will lead to a significant increasing cooling in 2070 or 2080. Variations of the galactic cosmic rays and cloud cover practically do not affect the climate. The quasi-bicentennial cyclicity of the TSI also provides simultaneous climate variations on all Solar system planets.