I would just lean it up against a rock next to my campfire. I am not wanting to do this routinely, only as a back-up if all else fails. I would move it away from the fire with a multitool or a bandana as a pot holder.

If I am going to hike with two nalgene bottles, why not replace one with an aluminum one and gain an additional method of purification at the cost of only an ounce or three?