What third factor producing both higher IQ and then industrialization are you suggesting?

Obviously you're not suggesting anything as silly as the industrialization causes all observed IQ changes, because that simply doesn't explain all examples, like East Asian countries:

A crucial question is whether IQ differences across countries are a simple case of reverse causation: Do high-income countries simply develop higher IQ’s? We address this question in a number of ways, but the most important is likely to be this simple fact: East Asian countries had high average IQ’s—at or above the European and U.S. averages—well before they entered the ranks of the high income countries. This is precisely the opposite of what one would expect if the IQ-productivity relationship were merely epiphenomenal.

Rindermann 2011: "Intellectual classes, technological progress and economic development: The rise of cognitive capitalism"; from abstract:

Based on their pioneering research two research questions were developed: does intelligence lead to wealth or does wealth lead to intelligence or are other determinants involved? If a nation’s intelligence increases wealth, how does intelligence achieve this? To answer them we need longitudinal studies and theoretical attempts, investigating cognitive ability effects at the levels of individuals, institutions and societies and examining factors which lie between intelligence and growth. Two studies, using a cross-lagged panel design or latent variables and measuring economic liberty, shares of intellectual classes and indicators of scientific-technological accomplishment, show that cognitive ability leads to higher wealth and that for this process the achievement of high ability groups is important, stimulating growth through scientific-technological progress and by influencing the quality of economic institutions.