I could see it contributing greatly to the advancements, though. Since it was colder, you had a shorter growing season in the northern parts of Europe and north america. This led to people spending more time near each other. After all, do you want to spend time outside in the cold or near a fire? I, personally, like my private bits and would prefer them to not fall off.
This led to less wages for farmers allowing them to be bought out or driven out by large land owners., so they moved toward a city (or slum) to keep and looked for work to do. Ostensibly, if we stayed spread out as farmers, we wouldn’t have had as much labor to fuel the industrial revolution and would have had fewer eyes of people looking at, for instance, weaving and then coming up with an idea to make it better, which allowed other inventors to stand on their shoulders and create better versions and even wholesale changes.
One thing that has been true for most of human history: The more people that interact with a technology, the faster it changes and gets adapted for other uses.
So, following that line of reasoning, I could see how the LIA could have been a boon to invention and progress in general without having to concentrate specifically on heat generation.