environmental conditions have a big impact on running performance and just as there are "morning" people and "evening" people, there are cold weather runner and hot weather runners.
However, hot weather tends to raise the core temp and so your heart is already working harder to pump blood to cool the body so it is ofen expected that running in cooler temps will result in faster times.
If you listen to post-race news, you will often hear of how the weather had an impact on the times - Boston is a classic. Hot day in Hopkinton means a longer time to reach Copley Square.
depends on how hot ... cold air is usually dry, warmer air contains more water, thus more oxygen and so lungs get more instant oxygen; however, once your body has to work too hard to cool itself, heat becomes problematic
For me, I run way better at 60 degrees than 20 or 80