Heat box/throttle linkage

No airplane does that. I think a filter would slow the airflow and cool the air too much. When it comes to carb heat, you want the maximum amount of heat to melt carb ice.

There was a lever which would turn on carb heat when the throttle was closed. Most folks removed it because it had the unintended consequence of allowing unfiltered air into the carb when it needed filtering the most - while taxiing. Since the throttle is almost closed while taxiing, carb heat was automatically applied, meaning the air coming in was unfiltered.