Thing is though... it's not a very efficient way of cooling down. Radiating heat is as a rule very inefficient. That's why we sweat, because then we don't radiate as much as conduct it. Which is vastly more effective.

The animals in the world that uses their ears and equalient cool them down using the airflow. There are many other ways of cooling down (like keeping cooler air "stored" inside the fur, rather clever).

It's not on a biological level the obstacle lie. It's on a thermodynamic level.