I'm not an expert, but yes we can and we do.
And so does the coral!
If a species of algae cannot handle high temperatures without generating chemicals like hydrogen peroxide which trigger the bleaching, then that species is ejected sooner and more frequently during warmer months, creating selective pressure for species that can.
To survive these conditions without getting ejected, the algae need to essentially run their photosynthesis process more slowly. They produce less chlorophyll per cell and create sacrificial 'photoprotective carotenoid pigments' which act like sunscreen and dissipate that potential sunlight energy as useless heat (coral has a few tricks too fluorescent proteins).
So the coral is actually in a delicate balancing act, selecting the most aggressive/productive algae which won't also try to kill it during summer. Corals will learn to be more conservative in their selection and algae will get more conservative themselves. We want this process to happen quickly enough so that we don't lose coral coverage and diversity in the coming decades / centuries, but we can be confident that on longer timescales the coral will adapt, assuming we don't get runaway warming.