Answer: In full sun locations, your container plants must be able to tolerate heat and intense sun. Some to consider would include tropicals such as lantana, tropical hibiscus (Hibiscus rosa-sinensis), and mandevilla. Additional annuals to try would include petunia, callibrachoa, salvia, and marigold, for example.
Your plants will do best in a larger container with ample soil volume. This will insulate the roots from heat and allow space for the roots to grow; the larger soil volume also holds moisture longer. When you plant, use a good quality potting mix formulated for container growing and consider using also a water holding polymer in the soil to help maintain steadier soil moisture. Plan on watering often in mid to late summer -- possibly daily.
Keep in mind that most window boxes are too small to allow for healthy root systems, the small size also does not hold enough soil to insulate the roots from the heat. And, when placed against a building, the plants also suffer from heat reflected off the wall. For these reasons, it is often just not practical to try to plant small window boxes on a hot western or southern exposure.
I hope this helps.
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