The fire at Miss Havisham’s house is indeed symbolic. It represents her passion, or her life-force. The house, like Miss Havisham, is wasting away. Pip first notices that the fires are extinguished. There is no life there.
I saw her pass among the extinguished fires, and ascend some light iron stairs, and go out by a gallery high overhead, as if she were going out into the sky. (Chapter VIII, 45)
However, on another day there is an actual fire lit. The fire is reluctant, as Miss Havisham is reluctant to have people there. This is the day she has visitors, because it is her birthday.
A fire had been lately kindled in the damp oldfashioned grate, and it was more disposed to go out than to burn up. (Chapter XI, P. 59)
There is more smoke than fire, and the fire seems to make the room colder rather than warmer. This is symbolic of Miss Havisham, who has allowed family into her house but is not warm to them. She is not welcoming them. She does not want them there, and she accepts them on false pretenses because they come on false pretenses. She thinks they are simply after her money.