Where im at, leaving a stethascope on the dash will result in a puddle of melted rubber pretty quickly.
Leaving literally anything on the dash will result in Extreme heat damage. Seen it before, not pretty. Lol.
Mine is in my bag that rides in the front seat of my squad. If I need it, I grab it and toss it around my neck for the call. When I'm done, it gets wiped down and put back in the top of my bag.
I often carry my scope around my neck, and I don't care if anyone thinks I'm a tool.