Likewise, would a water wave make the water it displaces more energetic? I'm guessing yes but it returns to its normal state once the wave passes, obviously.
At the first glance and following the definition of a wave (energy transfer without matter transport) the energy of the wave will only dissipate over space and the medium will not get warmer.
But in detail it is so that any disturbance of matter is accompanied by energy conversation from kinetic energy to a temperature increase of the medium.
This holds for any medium, be this water or air.