Is there another way to exhaust the air other than leaving windows or doors open? 

Yes. You may install up-dux vents to exhaust the air through your attic and out the roof vents. By exhausting cool air through the attic, you can reduce the temperature of this hot spot and make your home more comfortable. It is important to remember to provide adequate exhaust in the attic area. Provide 2 sq. ft. of relief for every 1,000 CFM of air delivery. However, it should be noted that up-dux do not provide adequate relief air during the hot peak season.