Why doesn't Scrooge start a larger fire in the office or repaint the sign outside of his business? What does this say about who he is?

He won't do either of those things for the simple reason that he is a moneygrubbing old miser. He is rich enough to be able to paint the sign and also to provide adequate heating in the office, both for himself and for poor old Bob Cratchit. But then he's also rich enough to provide Cratchit with a proper wage, and he won't do that either.
This tells us pretty much everything we need to know about Scrooge before he is visited by the three spirits. Money is everything to him. But it has taken over his life to such an extent that he can't enjoy his vast wealth. He lives all alone in a big old drafty house, feeling miserable most of the time. His miserliness over the sign and the heating in his office help to establish just what kind of a character he is and why he really does need to receive a short, sharp shock from the spirit world in order to see the error of his ways.