Hi figgygoose,
IMO, packing in straw is calling for rodents to come in, especially at winter time - they seek for hides and sheltered areas .
I pack them with dirt from the nurseries, because dirt won't attract rodents that much. And dirt holds the warmth acquired from the sun hitting the dark colored trashcan during the day.
I don't cover the top of the trashcans. I don't want to cook the trees. Even here, during the winter, I get some sunny days. During those days, the protected trees can get hot and cooked.
I'd rather use a higher container be it a trashcan or a 200L barrel, and fill it with dirt from the nurseries. You could pile two containers one above the other. Just stack them so that the top one doesn't slide and fall.
I would top the trees so that they fit inside the container.
Here on some of my trees, I used a dark plastic bag that I put over the trees . The bags had holes to keep some airflow .
One bag once had no holes, and I got lucky I caught the problem on time, as mold was starting to set in inside of the bag.
Here I can unpack my trees by the 1st of March, and I rush to unpack them. They really need the airflow.
This year, I left some empty trashcans longer around some trees to protect the stems a bit longer. But by now, all trashcans are removed, and the trees can breath as they want.
So far, so good ... This past winter (it is Spring already :) ) was luckily a mild one .