If the room that is connected to the closet you are going to be growing in is 85-90F, you are going to have heat issues that you are only going to be able to fix by drilling holes and mounting an intake fan to somewhere that's cooler and exhausting the heat somewhere else. Some people have to install air conditioners in their grow areas because of all the heat. It looks like you might have such the situation. There really isn't a simple solution to your problem. You could do blocks of ice with a fan blowing over it, but you'll have to change them out every 8-12 hours as they melt, but you still need to provide fresh air to the room or it will get stale.