the increasing concentrations of carbon in our atmosphere and oceans are a real thing, and they will have measurable consequences in the future. but, this is only one aspect in a complicated system, and for much of the planet, it's not even the dominant aspect. in the higher temperate latitudes of the northern hemisphere, it's actually a minor concern in understanding the weather for most of the year.
and, it won't keep us warm if the sun shuts itself off - not any more than a lighter will keep you warm in the dead of winter.
for better or worse, it seems as though we're currently emerging from a weak solar period, and, within the next couple of years, should expect the higher temperate latitudes to stop bucking the global trend.
for right now, expect a cold winter.