Is the sun cooler during a shallow cycle?
The theory is that the sunspot level is an indicator of the strength of the solar magnetic field. When the solar field is strong, the earth is better shielded from cosmic ray particles (high velocity charged particles). Higher levels of cosmic ray particles promote cloud formation, resulting is less solar heating of the ground. So low sunspot level = low solar magnetic field = more clouds = lower temperatures.
Of course the whole notion is ridiculous, since everybody knows that the Earth's temperature is solely determined by the CO2 level.
Still there is that pesky correlation, where the Maunder Minimum of 1650-1700 coincided with the Little Ice Age, and similar cool effects happening during the Dalton Minimum, but that's just crazy talk.