Start with the basics. Don't be distracted by the temperature. Make sure the basics are right, first.
Your symptoms are typical of poor connections or a failed battery. Could be something else, too, but start with the basics.
Check the battery cables and connections, both ends. This does not mean "glance at the top of the battery and if there's no obvious corrosion you are good". It means TAKE IT APART AND CLEAN IT. And do not overlook the ground connection to the frame, and the hot connection to the starter. People often make that mistake. "Battery's good, must be something else." Nope, BOTH ends need to be good.
And while you are at it, very carefully inspect the cables. Again, both ends. Corrosion can wick up inside a cable and rot it from the inside out. It's not readily visible from the outside. Look at the exposed end of the cable. Do you see corrosion there? If so, the cable may be bad. One way to find out is to get rough with the cable. Twist it, push it, bend it. If it feels at all "crackly", replace it. "Oh, but if I get rough with it, I might break it!" Good! If it's a good cable you won't bother it. If it's borderline, you want to break it.
If that's all good, get your battery load tested. A battery can show the correct voltage but not be able to support the load of a starting engine. This is especially true when it's hot.