Beater is slang deriving from beat-up, referring to something worn-out, dilapidated, weathered, or otherwise beaten up from age and use. I like the GNU CID definition, which Wordnik gives as
adj. worn by use into a deplorable condition.
The heater, in other words, was in such bad condition as to merit replacement, not repair or upgrade.
In my experience, beater usually refers to something mechanical: a vehicle, a tool, an appliance. By extension, however, since this is an informal term to begin with, it could be applied to most anything. Either a bent up egg beater or a tattered sleeveless undershirt might be a beater [of a] beater.
The police will tell you it’s not unusual for people to open their garage, find their expensive bike gone, and in its place find an old beater bike — the bike on which the thief arrived. —Tony Brown, "[Lessons from scuttling a Minneapolis bike theft scheme4", Minneapolis Star-Tribune, April 12, 2018
[P]eople sometimes buy an old beater truck… Say hello to the concept of a beater phone.—Catharine Hamm, "The best ways to keep in touch with home while you're abroad", The Los Angeles Times, September 3, 2017
And it wasn't his fault UC didn't rate, in the eyes of the Atlantic Coast Conference, or that the Bearcats play in a charming old beater of a stadium we don't fill. —Paul Daughtery, "Butch Jones commitment to Cincy was pretense", USA Today December 7, 2012