1) The notable event climate-wise in the early 19th century was the year without a summer, which, whilst breaking records of low temperatures, was caused by a volcanic eruption. Other than that, this period was quite similar to the 4 centuries before, so there is nothing special about “the early 1800s”.
2) Solar activity just does not add up. We haven’t seen anything like an increase that would explain a change by even +0.5°C (we’re on our way to 2°C).
3) Solar cycles are ~10 years, not 4 centuries, which is how long the little ice age lasted.
4) There is no indication that the Milankovich cycle has changed, which means that we would still be in that little ice age without greenhouse gases. Global warming cannot be explained by orbital mechanics either.
5) The average global temperature during that period decreased by ~0.2°C, or about -0.05°C per century; again we’re on our way to +2°C in ~1 century. The rates of change have nothing in common.
TL;DR: yeah, fuck all to do with solar activity.