Professional suits actually aren't that large for the person they're meant for, as the more tailored they are the better they look. (Mine was built off a duct-tape model of myself, and as such it's actually a bit tight because I'm a noob). The fur fabric gives the impression of bulk as it's usually a couple of inches long, and padding for body shapes is usually a snug pillow that conforms to the wearer. You can build and tailor a fursuit that takes into account space for a fan in the head or even a cooling vest, and people have done it, but cooling vests aren't super recommended anymore. You can feel cool to the skin while your core remains hot, and that makes heat exhaustion much harder to detect for the wearer and thus ironically more dangerous with a cooling vest on.
Most people just tough it out and follow some general safety rules: For every hour you suit, take a 15 minute break with the head off and get some liquids in you. Wear sweat-wicking clothes underneath like Underarmor. Ignore "Disney Performance" rules if you suddenly become overwhelmed with heat exhaustion symptoms. Shower, get six hours of sleep, and three meals a day. And a few days before a convention or event, hydrate yourself as much as possible anyway.