Solar forcings are not too small to explain twentieth century warming. In fact, their effect could be equal to or greater than the effect of CO2 in the atmosphere.
Benestad and Schmidt[45] concluded that "the most likely contribution from solar forcing a global warming is 7 ± 1% for the 20th century and is negligible for warming since 1980." This paper disagreed with Scafetta and West,[46] who claimed that solar variability has a significant effect on climate forcing. Based on correlations between specific climate and solar forcing reconstructions, they argued that a "realistic climate scenario is the one described by a large preindustrial secular variability (e.g., the paleoclimate temperature reconstruction by Moberg et al.)[47] with TSI experiencing low secular variability (as the one shown by Wang et al.).[48] Under this scenario, they claimed the Sun might have contributed 50% of the observed global warming since 1900.[49] Stott et al. estimated that the residual effects of the prolonged high solar activity during the last 30 years account for between 16% and 36% of warming from 1950 to 1999.[50] [...] the most likely contribution from solar forcing a global warming is 7 ± 1% for the 20th century and is negligible for warming since 1980.