Cut the linoleum into 2-foot-by-2-foot sections, using a utility knife. Start in one corner of the room and make straight slices down the linoleum.
Pry up one corner of the cut linoleum from the floor with a putty knife. Position a heat gun 2 inches from the adhesive under the pulled-up linoleum. The heat softens the glue for easier removal from the subfloor.
Place the putty knife under the pried-up edge and scrape the linoleum as you continue to soften it with the heat gun. Keep the putty knife as level as possible to avoid gouge marks in the subfloor. Scrape until you loosen the entire cut piece.
Place the removed linoleum square into a large cardboard box. Avoid placing the linoleum into trash bags that cannot hold the heavy material. Continue cutting small sections of linoleum and removing them with the putty knife and heat gun. Pile the cut remnants into the cardboard box.
Empty the box of cut linoleum pieces, depositing them into a large trash container before the box becomes too heavy.