Many locations and streets in London reference vineyards and wine growing, which is not feasible today. Summer is basically military campaign season. Could the expansion of the Roman Empire into Britain been helped by that warming period? There are many references to unusual weather patterns throughout history, but not a lot about how societies coped/took advantage of them.
I keep hearing about the English vineyards but I can't find any sources on it until about the 1000's when there was another warming period in the Medieval era. Rome did have a warm period as well that lasted from 250 BCE to around 400-450 CE, and according to historians like Theophrastus, it was indeed possible at the time to plant crops in places where they wouldn't normally grow. I've never seen anything about it helping or extending the campaigning season, though.
Unfortunately there's not a solid consensus on how much the end of this warming period affected Rome. It's certainly a probable cause for the mass migrations of Germanic tribes to the south. We do know through dendrochronology that the cooling climate was hindering growth in this period; if crops aren't as plentiful as they were before, people are going to look for new homes. This doesn't necessarily mean a violent invasion (although those did happen too), but either way a sudden influx of new people is a huge resource strain. It may or may not have directly caused West Rome's fall, but it certainly didn't help on top of everything else it was struggling with.
East Rome fared much better for about the next century or so. There was, however, a mysterious event that occurred around the 530's that was probably a severe volcanic winter. This caused widespread famine and most likely resulted in the first outbreak of the Bubonic Plague a few years later -- both of which devastated Eastern Rome and much of Europe, and helped to shut down any hope of ever restoring the empire.