I am uncertain about the heat sensitivity of propellants designed to replace black powder, but black powder itself fares quite well in the heat -- as long as it doesn't get hot enough to ignite.
Smokeless powder degrades rapidly when exposed to high temperature. It's affected by it. When the Germans invaded North Africa in World War II, they discovered that their small arms ammunition produced higher pressures because the powder was affected by the high heat.
I've read that German munitions factories began making special ammo for issue to the Afrika Corps, to counter this effect, but can't confirm it on the net. It may be apocryphal.
But black powder doesn't degrade in high heat. As has been noted, the greatest effect is probably upon the lubricant. I live in the remote Utah desert where temperatures can reach 110 Fahrenheit (43.5 Celsius) and humidity can be down to 6 percent. I've shot my cap and ball revolvers in such heat, and found that I have to use extra lubricant to keep fouling soft.
Normally, a felt wad lubricated with Gatofeo No. 1 Lubricant (named after me, but based on a 19th century recipe) between the ball and powder is sufficient. Under such extreme conditions, however, I've learned to put a light grease (composed of beeswax and olive oil) over the ball as well. This keeps the fouling soft and the bore free of fouling.
In a rifle with patched round ball, under such heat, I'd suggest a lubricated felt wad on the powder, with a lubricated patch holding the ball. The lubricant should be water-free if you plan to keep it loaded for more than a few minutes, to avoid rusting. Crisco would be fine.
A felt wad should NOT be used under conical bullets that have a hollow base, lest the wad be driven up into the bullet's hollow base and prevent it from bumping up to engage the rifling. The use of a felt wad under a hollowbased bullet probably isn't dangerous, but it will surely affect accuracy. I base this on personal experience years ago, with my .50-caliber muzzleloading rifle.
Rather than using a felt wad under a hollowbased bullet, simply fill the hollow with lubricant. To prevent contamination of the powder, a thin wad of waxed paper -- the kind sold on a roll to wrap food -- will be sufficient barrier. It will be consumed in the first few inches of combustion, I suspect.
In hot weather, keep your powder and caps out of direct sunlight. Don't leave them in your vehicle, where temperatures can reach 150 degrees or more. If you must, crack the windows and put them on the floor where the cooler air will be found. Cover them with a thick towel or blanket, for insulation. Keep them separate.
A cooler of ice would be good for storing powder and caps in a vehicle. Put them in Zip-Loc bags to discourage moisture and, obviously, raised above the level of the ice or any possible water.
Years ago, on a hot Idaho day, I got into my pickup after it had been parked for hours with the windows up. I immediately noticed green plastic parts all over the interior. My pressurized butane lighter had burst from the heat! Since that incident, I've gained a new respect for the temperatures that can be generated inside a vehicle.