First, you need to lerp between the current rotation and the default rotation. Use Time.deltaTime and a speed as t parameter.

Then, you need to decide when this is performed. I'd say when those two rotation are different which means the player moved the mouse, but with a timer reset every time the player actually move. It would look like that :

function Update()
{
    if( Mouse move )
        timer = WAIT_BEFORE_CENTER_WEAPON;

    if( timer > 0 )
        transform.rotation = Quaternion.Lerp( transform.rotation, defaultRotation, Time.deltaTime * speed );

    timer -= Time.deltaTime;
}