Turn off the gas stove. Allow the stovepipe to cool for 3 to 4 hours.
Wipe all stovepipe seams with a clean rag. Exchange rags when they contain visible dirt, grease or other contaminants.
Open a tube of high-temperature sealant by cutting its end with a sharp knife and puncturing the inner seal with a long sharp object. Slide the open tube in the body of a caulk gun.
Set the tip of the open tube on a clean stovepipe seam. Squeeze the gun handle to begin dispensing sealant on the seam. Pull the caulk gun along the pipe to cover the seam with caulk.
Drag a 2-inch paintbrush along the caulk to spread it along the seam. Inspect the caulk to ensure there are no voids in the sealant.
Allow the sealant to dry for the time specified on the caulk tube before turning on the gas stove.