Measure the barrel from top to bottom while it is sitting upright. Divide this number by two. Measure down from the top by this number and draw a line all the way around the barrel so you can cut it in half. Cut along this line with the jigsaw.
Turn the top half of the barrel over so the cut side is up. Mark a straight line from the top edge to bottom. Measure 14 inches to each side and make more vertical lines from top to bottom. Use the jigsaw to cut along the two outer lines, being careful not to cut into the rim of the barrel. Holding the jigsaw at an angle, cut along the rim between the two lines and remove the barrel piece. This is the opening of the chair where people will sit.
Turn the cut barrel top around so the back is facing you. Make another line down the center, then measure 8 inches to each side from that line and make marks on the top edge. Measure down 7 inches from the top at each of the outer marks and make more marks. Draw two vertical lines from the top to the 7-inch marks. Cut along these lines.
Turn the barrel around again so the open side is facing you. On both sides of the 28-inch opening, measure down 9 inches from the top edge and make a mark. At each of these marks make a 2-inch long horizontal line. Cut along the lines on each side. The plastic section from the horizontal cuts up to the top edge is going to get bent and form tabs for the arms of the chair.
Bend the tabs into place. Using the heat gun and wearing heat resistant gloves, heat the plastic tabs you just cut. Bend the plastic above the 2-inch cut away from you until you have approximately a 90 degree angle. Do this on both sides.
Bend the plastic sides down to create arms for the chair. Use the heat gun to make the plastic malleable and hold the plastic in place until it cools. Take your time heating the plastic paying close attention so that it does not melt or burst into flames. The tabs will overlap the chair arms. Do this on both sides.
Holding the arm in place, drill a hole through the tab and the chair arm. Place a washer on the bolt, insert the bolt in the hole and hold everything in place with the nut. Repeat on other side.
Take the bottom portion of the barrel and turn it upside down. Place the top part of the barrel on it, centering them so the edges are flush. Drill four holes through the bottom of the top barrel and into the bottom barrel. Attach with bolts, washers and nuts.