Install a glass door in place of your screen door if possible to increase the barrier between the outside air and inside of the home during cold months.
Close the sliding doors securely shut. Walk around the door with a lit candle to see where you have a draft. Check the bottom, sides or middle intersection where the two doors overlap.
Mark all of the areas where you have the air leak with some masking tape. Measure the approximate width of the gaps with measuring tape or a ruler.
Use insulation strips (also called weather stripping) of the same or slightly thicker width as the gaps you’ve identified to line the leaking areas. Insulation strips have adhesive on one side attached to insulation foam that helps keep the air in or out of an opening. It provides a tight cushion between the cracks and crevices of windows and doors.
Test opening the sliding door to ensure that it functions. It's OK if it's a bit more difficult to slide due to the insulation strips, since you can always remove the strips later. If you have too much trouble opening the doors, you need to replace it with a thinner strip of insulation foam.
Insert caulking compound into very thin, small cracks around the sliding doors where insulation tape won’t fit with a caulking gun. Push it in securely and remove the excess with a putty knife. Allow it to dry for four to six hours before opening the door again.