The info I have been looking at suggests 2ftX2ft as the height and spread for the tuberous begonia. I am thinking that perhaps your Begonia is possibly a sport or came along for the ride with one of the others you purchased that day. If it is that heat sensitive, it could be one of the Tuberhybrida cvs as they are usually a cross with one of the Andean species.
http://www.pacificbulbsociety....
[url=ahttp://www.gardening.cornell.edu/homegardening/scenef2e2.html]ahttp://www.gardening.cornell....[/url]
In answer to your question, I can only posit a guess. Since there are so many different shrub begonia species, I would think yes it is possible. (
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http://www.bradsbegoniaworld.c...
http://www.kartuz.com/c/2BEG10...
http://www.igarden.com.au/plan...
