A refrigerator is warm on the outside at the back because it extracts heat from the inside. The unit here is nothing different, only the room air is blown through the cold part, which cools down. The warm air at the back has to go out to the room so that it is cooler in the room overall, yes. That's what the exhaust hose is for. More warm air should go out, so it can come back in through an open window. So make a hole in the window or the wall for the hose, or seal everything nicely... ;-)