Autumn in Madrid is a life-giving season. Pleasant temperatures replace the stuffiness and heat. In September and October, it's still warm enough. A lot of tourists come to the city at this time. Don't forget these are the last months for bullfighting experience. Sometimes there is a light rain, but it does not affect general mood in any way since immediately after it the sky lights up.
In November, the real autumn is finally felt. The temperature decreases. At night, it drops to +4°C + 7°C. At the same time, the humidity level and the amount of precipitation increase.