Convection for air exchange?

I'm re-configuring my cabinet and switching out HID for LED and along with that I'm changing my whole exhaust system and was just wondering with a 10" hole at the top of the cabinet could I just use natural convection to let the heat escape from my cabinet?

Also, would the hot air pass through a 12" x 12" x 1" thick layer of carbon?

No.

Also, for convection, you'd need an equally sized cold air intake. Plus, with the carbon obfuscating the top hole the bottom would need to be larger.

400w real draw led keeps my tent 80 in a 70 room. 600w goes to 85.

You need to exchange the entire volume of your grow space every 5 minutes just to provide the plants with what they need. (This assumes a full space. If you had one plant in a 4x4 tent, you might get by with every 1-2 minutes.).

Exhaust heat out of top with a fan

Let cool air come in the bottom passively.

I know all the conventional routes, I was just curious how much air would move naturally, The openings for the intakes are larger in total than the exhaust...How this all came about was I was fitting a new fan and cut a 10" hole and was like damn, that hole's pretty big I wonder how much hot air would just rise out of it. That story wasn't all that interesting now that I typed it all out

Mr. Belvedere, you just like everything huh lol?

Tight pocket, put a carbon filter inside cabinet and run silver flex duct, or solid if you like, and put a fan outside the cabinet pulling the filtered air out. This will keep negative pressure in the cabinet to ensure no smell escapes.

Make your intake big enough to let in as much fresh air as possible without losing negative pressure. You can hold an incense stick outside the cabinet near an air leak and it should draw the smoke slightly in.

Where you exhaust to depends on heat. Experiment around.