Known. Basins of water stood beside the chariot track.
The Roman Circus of Carthage, in Tunisia, was a place for chariot races about 2,000 years ago. The track was about 470 metres long and 30 metres wide. Diggers found waterproof mortar on the bank in the middle of the track. Water basins stood along the track. Workers called sparsores dipped clay pots into the water and sprinkled the chariots as they went past.
The page says no one knows exactly how that cooling was organised.