Natives with long tap roots like the bright orange butterfly weed are completely unfazed by the heat, as are shrubs like crepe myrtle and caryopteris.
Liriope muscari has grassy foliage and spikes of blue or white flowers in the heat of late summer. It is especially accommodating as an edging or groundcover and there are some varieties with handsome variegated leaves (eg ‘Silvery Sunproof” ).
Many white flowers bloom in May, but the tiarella is one of the only ones to bloom so prettily in the shade.