Several techniques were employed to make conditions more tolerable before the general summer exodus to the hills became commonplace around 1840.

Bungalows were whitewashed to reflect heat, and many were provided with not one but two thatched roofs, one over the other, to help keep out the sun. From the 1780s, windows and doors could be covered with a new invention: screens of dampened, fragrant khas-khas grass, which cooled and perfumed such gasps of wind as could be made to enter, but relays of servants were still required to labour inside the buildings, tugging at punkahs, thick cotton mats that swung to and fro from all the ceilings to circulate currents of air.

The most spectacular and complex attempt to provide cooling, before the development of mechanical air conditioning, was an invention of the early 1830s of a man-powered version of the same idea called the thermantidote, ‘a wooden machine nine feet long, four feet broad and seven high’, which sat on the verandah outside a window. The window was removed and in its place a khas-khas mat was fixed. A hole was cut in this to take a funnel projecting from the thermantidote.

Inside were four fans turned by hand which drove the air into the room. To cool the air, two large circular holes were cut in the sides of the machine in which grass mats were fixed. Water was dripped from perforated troughs above onto these mats, and the surplus water fell into other troughs below to be used again in the troughs above. The thermantidote’s chief defect was that it required at least six coolies to power it, with others in reserve to take over from exhausted comrades.

Sources

Mike Dash, Thug (2005)

RV Vernede, British Life in India... 1750-1947 (1995)

oh hey, something that I actually know the answer to.

One of the most common responses of the British moving to India was, sadly or happily depending on your perspective, to die. Malaria, and later Cholera was endemic in India and many British officers, soldiers and merchants would travel out to India only to drop dead almost immediately. Even when they survived the initial bout of sickness, people were often permanently weakened or disabled by their encounter with the tropical climate. One British man, Richard Smith, wrote to his brother in 1827 that “There is something in this climate very prejudicial to the health of Europeans… I scarcely ever feel well… should that fever seize me, I must say there is very little chance of me surviving.” When people like him returned to Europe they were often delicate, their health destroyed by malaria and the various other fevers that afflicted them. The problem was so bad that there was even a separate medical category of the "tropical invalid." The physician Thomas Trotter described them as such "These persons bring with them to Britain, indelible marks of the effect of the climates they have lived in: dyspeptic complaints, and all their nervous accompaniments, are never failing diseases of this enervated people," and chiefly blames the Indian heat for their problems.

However, when a person arrived in India, according to the medical knowledge of the time there were certain rules that a person could follow to increase their chance of not falling victim to a climate that was out to kill them. According to the tropical physician James Johnson who wrote an acclaimed manual/medical textbook on the matter "The most dangerous effects of the new climate [can be reduced] by a strict observance of two fundamental rules – temperance and coolness." Both were designed to discourage sweating, which, according to cutting edge medicine of the time, stopped the liver from working, caused fever and led to death. Alcohol was held to cause sweating, making it bad. At the same time, coolness, or not exposing oneself to undue heat would preserve health.

So, how do we go about this. For the most part, Johnson urges his countrymen to "learn from the native." So the Indians wear "the light flowing robes of cotton, silk, calico," while British flannel is "inconvenient" and he bemoans the "tyrant necessity" of "continuing to appear in European dress," because of how incredibly uncomfortable it was. Europeans should likewise imitate Indians in not exposing themselves to the heat of the day. He describes this in full blown oriental fashion as the "Hindoo" retreating to his inner sanctum to gently perspire, drink sherbet and wait for the heat to die down so he can emerge. Similarly, substantial exercise was out of the question -- as he says "A perseverance in our customary European exercises, would prove highly injurious, and often does so, by greatly aggravating the natural effects of climate." "Passive" exercises had to be found which would not overstress the delicate bodies of the colonial overlords. The final point that he makes is on diet. Again, he recommends that like the Indians, the British should go vegetarian during their stay in India meat is too heating for the body to bear in India.

Sources: Thomas Trotter: A view of the nervous temperament

James Johnson: the Influence of tropical climates on the European constitution

Mark Harrison: Climates and constitutions

Mark Harrison: Public health in British India