Lots of good posts on this thread.
I have noticed a great many references to heat-induced illnesses in Union units during the Petersburg campaign from official & pension records. I have also found several references to their relatives dying of 'heat stroke' between 1870 and 1900 back in the Great Lakes region from death causes documented in old death records. It's been a perpetual problem. I suspect that injuries and death from heat-induced illnesses outnumber ailments related to too much fluid intake by about 100,000:1, just my educated guess. I write as a retired emergency physician. The majority of all my patients were at least mildly dehydrated on arrival to the ER for whatever their problems were, from sprained ankles to heart attacks. That's why so many emergency patients have IV's started even though there seems to be no pressing need for it, it's a whole lot easier to start an IV before someone passes out.
The hottest work I myself ever did was laying concrete blocks outdoors in Austin TX on a summer day when the air temp was 100 and the humidity about 30% with a steady wind of 20-30 mph blowing. I was 19 at the time, wore long sleeves and long pants with a broadbrimmed hat, drank copious amounts of water, Mountain Dew and beer, along with Fritos corn chips. I did not have to carry heavy objects long distances, everything we used was stacked up right next to our work site. If I had to carry bags of cement or blocks longer distances, I couldn't have done that job. I was also jogging a mile or two every day, usually in the morning before it got too hot. Outside of being tired at the end of that day's work, I felt just fine. My dad worked side by side with me, he was 55 then, and worked shirtless and hatless. He was rather ill by the end of the day, and the next day had a 2nd degree sunburn. And to think he had served with the US Army in the South Pacific, I don't know how he survived.
Now that I'm 63, there is no way I can repeat that feat of strength & endurance, and live to tell about it. Older people are more prone to heat-induced illnesses. Remember there were 10,000 extra deaths in France during a 2003 (IIRC) heat wave there. Most of those were elderly people. After Hurricane Katrina hit New Orleans, many of the deaths were not directly related to the storm but to the heat & humidty combined with a lack of water, a very high percentage of deaths there were in the over-70 population. This is important for re-enactors over the age of 50 or so.
The quickest rule of thumb to maintain adequate hydration is the Army way of monitoring for concentrated urine, then drink more water until urine is less concentrated. Severe dehydration medically (without testing or measuring anything, just using your regular senses) would be sunken eyes, dry mouth, decreased skin turgor with 'tenting' - pinch the skin lightly and release, the skin will not rebound as it usually does, a pulse not as strong as usual (takes experience to know what that difference is.). The previous medical signs are consistent with severe dehydration. However, in hot weather many people will get severe heat induced illness long before they are that dehydrated, so you really don't want to wait that long.
And you cannot rely on feelings of thirst to determine whether or not you are dehydrated. Some of the most dehydrated patients I have had were not thirsty in the least. Some of my thirstiest patients just had dry mouths, and needed no extra fluid.
And even if you are perfectly hydrated, you can get heat-induced illness. There is a limit to what the body can stand. Heavy exertion in someone in very good physical condition under hot/humid conditions can bring this on very quickly.