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There's a pretty large combination of factors that went on from what I remember. Partly it just plain didn't get that hot that often in the UK or France back then. Partly they wore entirely different undergarments that layered to keep sweat off their actual clothes and keep them cool. Partly the summer clothes were often flowy or puffy which helped move air near the skin. And partly the fabrics they wore were different. Things like linen and cotton were the go tos. Even the linen itself was different, modern linen has shorter fibers and is much lighter.

After the great renunciation (when men started wearing the modern(ish) suit) you start to see a lot more references to taking off layers either to cool off or to keep them clean or whatever. You also start to see variations in really hot places like the American deep south and Bermuda to deal with climates that get way way hotter than Europe with its nearby seas and cooling prevailing winds.

Please note that all of this may be wrong and I am entirely going off what I can remember off the top of my head.