Why Apollo 11 was launched in summer? (Performance question)
The temperature of the environment doesn't have a significant impact on the performance of a rocket engine. Air breathing engines have better performance in cold air because the mass density is higher at a given pressure, which allows them to ingest more air, and because the thermodynamic efficiency of a heat engine increases when the temperature of the cold side decreases.

A rocket uses oxidizer from a tank, and the thermodynamic cold side temperature is the temperature of the propellant before it gets burned. Thus, atmospheric temperature doesn't change rocket performance like it does for air breathing engines.

Remember that rockets aren't pushing against the air, they're pushing against their own exhaust. Atmospheric pressure slows down the escape of the exhaust, reducing thrust. Rockets will produce more thrust in a vacuum than they will in the atmosphere.

The main concern for timing the launch of Apollo 11 was making it happen as soon as possible, both to beat President Kennedy's promise to land a person on the moon before the end of the decade, and to beat the USSR to the moon.