Long term solar magnetic cycle changes modulation of cloud cover is mainstream as it can explain the data.
The following is strong support for a mechanism such as solar magnetic cycle changes which can modulate planetary temperature. Note the mechanism in question is capable of cooling the planet in all climate conditions.
http://dx.doi.org/10.1016/j.palaeo.2006.08.008
“Millennial-scale paleoclimate cycles recorded in widespread Palaeozoic deeper water rhythmites of North America” by M. Elrick and L. Hinnov
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“Rhythmically interbedded limestone and shale or limestone and chert (“rhythmites”) are a common feature of many deep-water Phanerozoic carbonate marine deposits. Seventeen different Palaeozoic rhythmite successions from across North America…”
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“…If our short-term paleoclimatic interpretations for the rhythmites are correct, then it is apparent that millennial-scale climate changes occurred over a very wide spectrum of paleoceanographic, paleogeographic, paleoclimatic, tectonic, and biologic conditions and over time periods from the Cambrian to the Quaternary. Given this, it is difficult to invoke models of internally driven thermohaline oceanic oscillations or continental ice sheet instabilities to explain their origin. Instead, we suggest that millennial-scale paleoclimate variability is a more permanent feature of the Earth's ocean–atmosphere system, which points to an external driver such as solar forcing.”
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