The problem of global climate change in the 20th century and its nature is under discussion. The issue of anthropogenic nature of global warming in last decades, as well as contribution of natural factors and solar activity, is of special importance. IPCC experts (Climate Change 2007) concluded that the Earth's climate in the 20th century changes due to the increasing СО2 content caused by anthropogenic activity. A new concept of the effect of solar activity on parameters of the Earth climate system managing the energy flux outgoing from the Earth into the space in high-latitude regions is described. A physical mechanism and a model of the effect of solar activity on climate parameters and heat content of the atmosphere are presented and discussed. Long-term variations of the temperature and heat content in the troposphere are analyzed. The probable contribution of solar activity to variations of the tropospheric heat content and the Earth's climate system in the 20th century is estimated.