Standard solar models predict a solar luminosity that gradually increased by about 30% over the past 4.5 billion years. Under the faint Sun, Earth should have been frozen solid for most of its existence. Yet, running water is observed to have been present since very early in Earth's history. This enigma is known as the faint Sun paradox. We show here that it can be partially resolved once we consider the cooling effect that cosmic rays are suspected to have on the global climate and by considering that the younger Sun must have had a stronger solar wind such that it was more effective at stopping cosmic rays from reaching Earth. The paradox can then be completely resolved with the further contribution of modest greenhouse gas warming. When we add the cosmic ray flux modulation by a variable star formation rate in the Milky Way, we recover the long-term glacial activity on Earth. As to the future, we find that the average global temperature will increase by typically 10¿K in the coming 2 Gyr.