I am a French horn player. As such, I remembered that the mouthpiece should be the same temperature as the “con cert” hall. Accordingly, when I played, I held the mouthpiece in my hand to get it and keep it at room temperature.
Prior to sounding the Shofar, I hold it under my arm resulting in two benefits: 1) mouthpiece is at room temperature; 2) Shofar is not seen by the congregation.
