It may be that your birdbath planter is too shallow and thus the roots can't go very deep for a more dependable supply of moisture. The metal getting hot can be a contributing factor also. If you are going to keep the planter in a sunny location you might try a more drought tolerant plant like one of the succulents. Some produce small blooms and some will also trail over the sides. The moss rose or its close cousin portulaca should also be able to take the sun and shallow planter if you keep the soil moist but not too wet.
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