The field area of the Earth’s lower (<3.2 km) clouds is shown to correlate significantly with the intensity of galactic cosmic rays in 1983–2010, with the sign of correlation reversing in 2003. The same effect is discovered in the correlation between air temperatures in various regions of the Earth and the relativistic electron fluxes with energies of 30–300 KeV that precipitate in winter (December–February). An energy-balance climate model is used to estimate the possible contribution of lower clouds to the globally averaged temperature in the indicated period. It is shown that the consideration of lower clouds as a radiative forcing allows one to explain the global warming of the last 30 years without employing the hypothesis of anthropogenic greenhouse heating.