Usually in the days following a good-sized storm, we get a rush of colder air moving into the upper levels of the atmosphere. That makes it easier for clouds and storms to form because when pockets of warm air rise from the ground, it'll keep rising farther since it will stay warmer longer relative to the surrounding cold air.

If the air is really unstable (read: really cold air moving in), it can create storm cells with heavy rain with frequent lightning and/or hail. These storms tend to form in the afternoon and evening after the sunshine has had a chance to warm the ground and get the process started.