the text you quote misrepresents what the NASA scientist's said ... unsurprisingly as you regularly rely on dubious information.
the cooling referred to by the NASA scientist is in the thermosphere ... as in 65+ miles and beyond above the earth's surface. in contrast there is still a significant warming trend in the troposphere (0-11 miles above the earth's surface).
the original place where the NASA scientist's comments appear makes no mention of little ice age or temperatures/weather on the surface of the earth ... nor do scientists find a direct relationship between warming/cooling of thermosphere and the surface of the earth/troposphere.
whether or not the predictions of a grand solar minimum will come to fruition in the coming decades and whether or not that could lead to a cooling effect ... the amount of cooling predicted from such a grand solar minimum has predicted to be a small fraction compared to the warming due to anthropogenic greenhouse gases.
and again ... the little ice age was a localized event in the upper northern hemisphere, not a global event as we're currently observing.