How to ride when the weather is hot?
Several questions, several answers:


Is there a temperature above which you don't ride


Yes, for me that's about 45°C. At that temperature where I live (Australia) the air is usually so hot that even wearing glasses it's hard to blink often enough to keep my eyeballs from drying out. Wrap-around glasses, complete skin coverage, and riding slowly is the only way to go. Or it's just before the rainy season and sweat is pouring off me just standing in the shade, so I don't go outside if I can avoid it.


Do I have to be cleverer than my usual (water)


Ideally, yes, regardless of whether you're riding. But 35°C is not especially hot, it's more that it is useful to pre-hydrate and make sure you're drinking to replace sweat. My usual is to buy cordial powder and add salt until it's undrinkable when I'm at home testing it. When I'm riding it starts to taste good, so I drink it. "electrolyte drinks" that work taste foul when you don't need them, if they taste like soft drink they're purely there to replace the sugar and are thus a waste of money. You should also be drinking 2-3 times as much water as electrolyte drink. But again, at 35°C you should be able to ride an hour or more without issues (I ride 45 minutes home from work at that temperature in the summer, and drink before the ride and after, rarely during).


Do you know/recognize symptoms of overheating?


This is important. If you start to feel weak or have a headache you should stop, drink and cool down. If you stop sweating you're about to die, so you should immediately seek cool shelter and warn the people present (there must be people present) that you're suffering heatstroke and may pass out. Note that "sweat evaporates as fast as it appears" and "not sweating" are very different things. I find my back will generally stay wet up to about 40°C, and above that I try not to ride very hard because my body and especially my brain does not like getting above 40°C so I need to sweat just to stay alive, forget exercising.


Is it necessary to stick to shadier routes?


Anything you can do to stay cooler while riding is good. But note that riding close to building or on roads "in the shade" is often no better than being in the sun as they will reflect and absorb/re-radiate heat. Trees are good, riverside or on a path near a creek (even a dry creek) are better. Mostly, pay attention to how hot you feel.

I took photos last summer of heat blisters on my hands from resting on the brake hoods of my bike. That was at only about 38-40°C, but riding through a built up area with lots of shiny buildings and fingerless cycle gloves - you could see that the blisters were where bare skin had touched black plastic hoods. The blisters were really annoying to work around while they healed.


Is pouring water on yourself necessary, or a luxury? 


It's a waste of water, unless you have lots. A sock around a waterbottle, wet, can help but if it's hot and dry it won't help much, or for long. Keep the water for when you need it.


Do you ride without a helmet?


Not in Australia, where the law requires a helmet. I would consider it, and sometimes do, but I much prefer a helmet cover with a wide brim, then a headsock under the helmet to stop the sweat running into my eyes. It's much easier to wash or swap a sweatband or head-covering than to clean a helmet, especially if you're riding in the heat every day.

Clothing

The hotter it is the more I cover up. I'm a white guy, so in theory my skin is more reflective than black skin, but forget it, if I don't cover up I get way too hot. 

At moderate temperatures I don't bother, riding home from work I just accept that I'll get hot and since it's a known journey if I get home uncomfortably hot that's bearable. So I wear a white, long sleeve t short and white knee-length cargo shorts, plus helmet cover.

But when it's hot, usually I'm touring, so I wear the full kit. Head covering as above, then a long sleeve white t shift (cotton is fine, and SPF 50 or higher is better (in Australia we get SPF rated clothing)). I will attach that to white gloves, buying the lightest, baggiest gloves I can find. Strangely, dishwashing gloves are more available and work better than gardening gloves. I wear cycling glove under them, because the offer basically no road protection. Then I wear cycling kicks with long, baggy cotton pants over the top. Those tuck into my socks. Basically the only skin you see is my face, and not a lot of that.

Hydration

I prefer to drink enough that I have to stop and pee every couple of hours. If the pee burns I will drink right there until I can't drink any more without throwing up. This is when I will normally drop a film canister full of cordial powder+salt into my drink bottle, drink that, then straight water until I'm full. The goal is to get that water into my bloodstream as fast as possible.

You should never, ever get to that stage just riding at 35°C. That has only happened to me when I've been at the end of a long day touring after making a mistake and having to ride further, harder, than I expected.

Time of Day/ Avoid the darn heat

Finally, and most importantly, if you can avoid riding when it's uncomfortably hot, do that. I have flexitime at work, and in the hot part of the summer I will start later and finish later so I'm not riding home when it's hottest (normally I work 7am-3pm, but much over 35°C I'll start between 0830 and 1000, so I finish later). When cycle touring I'll either ride early or ride a split shift. I'll start at first light (30-60 minutes before dawn) then ride until I'm hungry, tired, or hot. Then I'll stop and spend the day trying to avoid the heat while being a tourist, and possibly ride again when it cools down.

If you're working and riding for exercise, do it before or after work/office hours. First light is a great time to be out, you'll see any local wildlife before people drive them out of sight, and it's a very calm time of the day in most places. Or follow the crowd and go out for a ride after work. There's more people, less wildlife, and it's usually hotter, but that is relative to dawn, not midday, it's still a lot better than riding at 3pm.