That's too simple of an explanation for me. Basketball players go hard. As hard as they can. NBA finals. Their bodies don't have "extra effort" to exert when it gets hotter. What happens when it gets hotter is they slow down. Just like triathletes slow down when it gets hot.
Hmmm... I would say there is not an "extra effort" they can give during a normal game, but a game played in 100 degree heat can be much more taxing -- both during the game and recovering afterwards -- than a game played a room temperature. Lebron said he felt like he had played a whole game by the third quarter. It's not just slowing down. Your system is also being taxed by having to cool itself.