The forced air in a furnace is to push the air around the house from the heat exchanger and suck it back from the return registers. It doesn't do anything for exhaust gases, at least mine doesn't.
That may have changed over the years though as they've tried to squeeze every last % of efficiency out of the oil. But if that's the case, it's a safety hazard since you're just a blower motor failure away CO poisoning.
Mine operates purely on the heat of the exhaust gas.
I see what you're saying though. At the very least though, do what you can to:
a) insulate the part of the chimney that goes thru the attic. It looks like you have a brick exterior. If that's true and it's not just decorative, you probably don't have a lot to worry about until you get into the general vicinity of the attic.
b) besides fire resistant insulation, try to create as wide of a diameter as possible to separate the piping from the soffits and roof.
I honestly think you would have been better off building a masonry chimney, but now you're talking the big bucks. That's how this house was built.
At one point I was a little concerned with CO infiltration since even masonry eventually gets cracks. So years ago I got a buttload of CO sensors. I would definitely advise that for you too. Think of the kitties. Heehee
