|I have canna lilies, dahlias, asiatic lilies, and other|
|Cannas and dahlias are usually dug up in the fall after frost kills the stems, the stems are trimmed and dirt shaken off, air dried at room temperature for several days, then packed in a single layer in dry shavings and stored dry for the winter at about 45 degrees. If stored too cold they will rot and if stored warmer they may try to grow prematurely. This process also allows you to replace the soil in the container every spring which is important because they both need a rich soil to grow well.
Asiatic lilies should undergo a winter chilling period in order to stay healthy. In a container, they could be stored in a location that is above freezing but below about 40 degrees. You would check the soil regularly and only water very lightly if needed to prevent the soil from drying out completely. If too wet, the bulbs will rot. The lily bulbs never go fully dormant so they are not lifted as this would disturb them and damage their roots.
Each different type of "summer bulb" has its own requirements, so depending on the actual temperature in your storage area it may or may not work for you. You might want to use a min-max thermometer to check on the temperatures. You should also check your stored bulbs periodically to cull any that are rotting and to make any adjustments to their storage conditions as needed.