I have a small wood stove with a 4" flue pipe going into a fireplace opening which leads to a masonry chimney built with a 12" square flue size. Right now there is no damper on the exhaust from the stove. Would I be able to get significantly more heat out of this stove if I adjusted the exhaust ?

The flue pipe comes out a 2' pipe straight out the back of the stove and into the fireplace opening. I just have a piece of plywood covering the opening to the fireplace  with an 8" hole for the flue pipe to go thru. Am I losing alot of heat with this setup ? The stove has a firebox size that is less then 1 cubic foot. I know this isn't idea by any means but I am trying to get the most out of what I have available right now.

Any advice would be great. As you can see I'm new to wood burning.

Here's some reading:

https://chimneysweeponline.com/hoosst.htm

https://chimneysweeponline.com/hounlfp.htm

https://chimneysweeponline.com/hostainlessliner.htm

And of course the Arfcom of woodstoves and chimneys:  http://www.hearth.com/talk/

Bottom line:  Yes, you'll need to reline the masonry chimney both for stove performance, safety and to meet current NFPA requirements.

Good luck!

Ideally you should put a liner in your chimney.  The combo outlet/flue your burning is ripe for creasote build up, BE CAREFUL!  A chimney flue that big will stay cold, for the amount of heat you're putting out, this equals creasote!