If you read accounts written from the 16th through the 20th centuries in Virginia, Washington D.C. and other parts of the United States south of the Mason-Dixon Line, they endured summer conditions with a variety of means. These included leaving overheated cities for rural retreats, the architecture of their buildings, the fabric they wore, and other assorted means. Some, however, did not endure. They died of heat-related illness just as people continue to do today, albeit at higher rates.

/u/chocolatepot is the flair that comes to mind for historic fashion and clothing, but Colonial Williamsburg offers some insight into what you're looking for:

"In the sultry climate of Virginia many, even the upper classes, chose washable linen or cotton clothing for informal wear. A traveler in the early 1730s described the summer clothing of Virginians: 'In Summertime even the gentry goe Many in White Holland [linen] Wast Coat and drawers and a thin Cap on their heads and Thread stockings [knitted linen]. The Ladyes Strait laced in thin Silk or Linnen. In Winter [they dress] mostly as in England and affect London Dress and wayes.'"

Consider too, the way architecture helped fight the summer conditions. If you investigate well-built homes from the 18th century onward in the American South, you'll tend to find light buildings with high ceilings and large windows. You'll find expansive porches with ample shade. The principles behind these designs are to allow airflow and ventilation. That tends to provide cooler conditions. Even something as simple as painting a home white could make it much cooler.

A modern building might have sealed windows, low ceilings, concrete construction instead of wood, and no porches or shady spots. Without air conditioning, they'd be difficult to enjoy in warm weather.

They also coped (or didn't) by various other means. The Battle of Monmouth during the American Revolution is known partially because of the extraordinary heat of June 28, 1778. In a letter home, Sir Henry Clinton (the British commander) wrote that it was 96 degrees in the shade during the battle. Of the battle's approximately 500 deaths, about half were due to heat-related causes. Horses also died in numbers (including Washington's own), and accounts of the battle describe cavalrymen riding naked from the waist up.

The memoirs of indentured servant William Moraley describe how 18th century Philadelphia sold meat on Sundays only in order to cope with the effects of the heat on that particular food. Moraley also wrote that on one day in 1730, eight people dropped dead on a single day due to the heat. It might also have been due to a popular belief of the time: "It is dangerous to drink Water at this Season, hot Liquor being more proper, to allay the Thirst."

What comes up again and again, however, is the idea of a retreat from the town ─ whether simply to a quiet riverbank or to a country house would have depended upon a person's means. In the 1730s, Moraley wrote, "The [Delaware] River is supposed to have its Rise from a Lake, in the Mountains of Canada, and is believed from its first Spring to the Capes, in its Windings, to be above 2000 Miles in length. In the Heat of Summer, nothing affords a more pleasant and delightful Prospect than it does."

Thanks, /u/The_Alaskan!

The first thing to address is the clothing itself: historical clothing was not as heavy as it looks. (Or not always - they did wear heavier clothing when it was cold.) Yes, they wore more layers and covered more of their skin than we do in the heat, but they were not wearing the equivalent of a winter jacket at all times. During the 18th century (which I'm looking at as you mentioned the Founding Fathers), men and women wore a linen undergarment at all times: the men's shirt was cut to above the knee and with long sleeves and a high collar; the women's shift was a bit longer and had a deep neckline and sleeves just below the elbow. Linen is smooth and cooling, pulling moisture from the skin and out to dissipate. On top of this, men wore a waistcoat and breeches, and women the stays (corset) and petticoats; then on top, for men the coat, and for women the gown. And that sounds like a lot, when you think about it on a hot day when the air isn't moving! But in practice, all of these could be made of fairly light and breathable materials. Linen clothing was not high-status and therefore was not frequently preserved, but we do have a few examples; we also have homespun cotton menswear, and we know that women were wearing muslin gowns from at least midcentury. (These were fitted. In the 1780s, loose, unfitted "chemise gowns" that were held in with a sash were a more casual and even cooler alternative.)

Another option was simply not getting dressed fully. English travelers reported that in the southern colonies during the summer, men sometimes went out and about without coat or wig (usually replacing it with a loose cap, which would satisfy the requirement of having one's head covered as well as providing protection from the sun), and women in loose jackets without stays. If at home, undress was even more acceptable: men and women could wear lightweight wrapping gowns with only the base layer underneath, or shirt and breeches/shift and petticoat. Field slaves were often assigned only the latter outfits, occasionally being assigned a summer jacket to wear on top.

Linda Baumgarten's What Clothes Reveal was my main textual source here: it's the go-to book on specifically American dress. It's an excellent read and you may find it interesting!