A marginally operating system will fail in hot weather. Have the system examined by a qualified technician. Newer models have cabin air filters that clean the air entering the heating and air conditioning system. Check your owner's manual for location and replacement interval.
The greatest cause of summer breakdowns is overheating. The cooling system should be completely flushed and refilled about every 24 months. The level, condition, and concentration of the coolant should be checked periodically. (A 50/50 mix of antifreeze and water is usually recommended.) DIYers, never remove the radiator cap until the engine has thoroughly cooled! The tightness and condition of drive belts, clamps, and hoses should be checked by a pro.
Batteries can fail any time of year. The only accurate way to detect a weak battery is with professional equipment. Routine care: Scrape away corrosion from posts and cable connections; clean all surfaces; re-tighten all connections. If battery caps are removable, check the fluid level monthly. Avoid contact with corrosive deposits and battery acid. Wear eye protection and rubber gloves.