The results of mathematical modeling, which demonstrate the response of the temperature conditions of the atmosphere of the North hemisphere to the changes of the solar activity, are presented. The calculations with the help of the ECSib climatic model (ICM&MG of SB RAS) were carried out. In the course of calculations, the influence of the solar activity was taken into account on the basis of the model of the solar activity effects on climatic features of the troposphere. According to this model, the intensification of the solar activity brings about an increase in a difference of electrical potential "ionosphere-Earth" and appropriate redistribution of the charged nuclei of condensation in the troposphere, changing the water vapor state and forming the cloudiness. The resulting cloudiness changes the radiation balance. The main attention in the analysis of the results is given to the troposphere response in high latitudes to helio-geophysical perturbations for the cold period. It is shown that a similar mechanism is capable of changing the temperature conditions of the troposphere in high latitudes.