You do need to be careful. Someone posted somewhere on BF in the last few weeks about a collapse he suffered on a ride. Almost certainly heat related. I was on a ride last weekend and felt really thirsty as I got to the top of a hill so I stopped to take a rest and a drink. As soon as I got off the bike I felt light headed and had a hot, tingly feeling running up and down my arms. Yikes! I took a long rest which had to be in the sun and I emptied my water bottle. Shade was called for but there was none available. After I felt steady again I proceeded slowly for a couple more miles where the shady area of the path started and shortly after that a water pump was available. I filled my tank again and the well water was much cooler than I expected which helped (tasted awful though). I was about 2 miles from home at that point and was easily able to take it slowly home without any further trouble. You have to take any sign of heat distress very seriously whether in yourself or a companion.
Most of it, I think, is just staying properly hydrated. Simple overheating from exertion is something your body will naturally take care of by refusing to continue at the same pace. Dehydration is far more serious as the OP's report shows. I was at an outdoor event some years ago when a young man rode up on a bike. He had ridden 18 or so miles in some dreadfully hot conditions to get there and started complaining about symptoms similar to mine above and worse. As it happened one of the gentlemen in the group I was with is an ER doctor. He examined the young man and recommended calling an ambulance. The "patient" objected at first and then relented. We made sure his bike was secure for the night and when he showed up the next day to retrieve it he was thanking our doctor companion profusely because he did indeed need an emergency re-hydration in the ER and had a pretty close shave with more serious trouble.
If you are sweating your hydration level is not too bad but you could be flirting with disaster even then. Once you stop sweating you need to act fast and you never should wait that long in fact. The trouble is that in very humid climates your sweat evaporates slowly so you could feel wet for a long while after you stopped sweating. In very dry climates it evaporates so quickly you can't be sure you are sweating and you can't know when you stop sweating. So a better rule of thumb is to just drink, drink, drink. Drink so much that you have to urinate every hour or so. Then you should be ok.
Oh, and while it was a bit cooler this weekend I carried twice my normal water supply and made sure to drink it all. Trying to follow my own advice....
Ken