Cover the top of the chimney with a piece of sheet metal that has been bent and formed to fit over the flue where it protrudes from the top. You can make your own cover or buy a commercially manufactured one. The cap needs to stop rainwater from getting into the chimney but also allow some air to move in and out. If the cap is airtight, it may cause condensation and deterioration inside the chimney.
Cut a piece of rigid foam insulation to fit into the chimney thimble. The thimble is the fixture in the side of the chimney into which a stovepipe goes when the chimney is in use. Fitting the rigid foam into the opening will prevent warm air from going up the chimney. For extra sealing, caulk around the edges of the insulation where it meets the sides of the thimble.
Open the cleanout door at the bottom of the chimney and inspect the inside with a flashlight. Clean out any ashes or soot that have accumulated at the bottom of the chimney. Be sure that the cleanout door is properly closed and sealed to protect the chimney over the long term.