Answer: Rex begonias are tropical in nature, sometimes called tender perennials. They can be overwintered indoors in your gardening region but must be potted up and moved inside before nighttime temperatures drop below 55F. If the tops of your plant have died down, I suspect Jack Frost has already visited your garden. If you decide to plant begonias again next year, be sure to take them indoors by the end of August.
Best wishes with your garden!
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