Contrails contribute to heating because they block light emmited from Earth's surface from exiting the atmosphere. It is the same mechanism by which natural cloud cover contributes to heating.

During the day, the effect is largely neutral with respect to warming. Clouds will block some sunlight and block some reflected light, net effect is roughly zero. During nighttime, however, they only block the Earth's surface radiation from discarding energy to soace and thereby act like a blanket, trapping heat. It is the reason why overcast nights do not cool as much from the day time high temperature.

Fun fact, the days after 9/11, where all US flights were grounded, had a 2-degree Celsius increase in the range of temperatures experienced from the daily high to nightly low compared to the surrounding days with normal levels of air travel.