My train of thought is rather simplistic about this,
but if the sun’s magnetic sphere of influance is in flux, & with our iron metal core & magnetic fields, I can see the temp. change due to the movement of these. Like the way that we get electricity by moving a magnetic field around a metal core and windings around the core. One of the by-products of this is heat, ergo climate change. and we did not do a thing to do this either...
JUST IMHO!!
The propsed mechanism that does seem to make some sense is that additional solar activity "blows away" cosmic radiation we get from interstellar space. That cosmic radiation has been demonstated to trigger clouds on earth, thus cooling it. So high solar activity, although not directly giving us any meaningful energy from the sun, nevertheless changes the climate because it prevents cloud formation.
It's an interesting proposition, and has some experimental and measurement backup to it. But it will take significantly more study before the conclusions are bullet proof.