Finding an aerodynamic shape

Suppose you took a straight arrow shaft made from plastic and suspended it from a very tiny string dead center through the nose. The shaft would be straight with a flat nose and tail. Now you turn on the fan and speed it up to about 200 miles per hour so the arrow is hopefully flying straight against the wind. Adjust the angle of the wind tunnel to best approx gravity forces on the arrow. Now turn up the temperature of the incomming air so it is just hot enough to start softening the hard plastic arrow and allowing it to slowly change shape in response to the rushing air. Would this arrow eventually find the most aerodynamic shape? Or would it just distort all to hell?