ヒーターがつけてあります。a
ヒーターをつけてあります。b
These are both natural and grammatical in the standard Japanese. This is not a dialect It's just the difference in subjects.
In a, the speaker is using Vてある almost like an adjective that means "of the state of being Ved." Here, the V is "turn on," which makes the quasi-adjective (not an official term) "the state of being turned on" And what is in this state? The heat.
In b, the subject is the person who's left the heat turned on. ている can take the place of English perfective aspect (have Ved) in Japanese. When the verb is transitive, you can make it てある to mean "have left Ved."