We study variations of solar activity (sunspot numbers W) and anomaly of global temperature (GT) to detect a connection of their time variations on different time scales (including trends) to understand cause of global warming. We use a method of non-linear spectral analysis that is capable of making a self-consistent selection of trends, non-stationary oscillations and identifiing time intervals of development of non-linear processes (appearence of oscillations of large amplitude) in data. Analysis shows that trends of both spectra contribute main part to the data changes and show correlated increasing of W and GT during the studied interval. Cause of Maunder Minimum and present global warming is regime change (from epoch of damping to epoch of building up) of the powerfull oscillations at T = 1000 yr. from the GT spectrum. Besides, time changes of GT and W has different type of connection in different range of periods T: non-stationary oscillations from the spectra of W and GT at T = 10 yr. and T = 30 yr. vary in opposite phase, at T = 22 yr. vary in phase. The latter means different influence of odd and even 11-yr solar cycles on anomaly of GT (warming and cooling accordingly).