A few internet nutters putting "carnitas" in the title does not make it so. :old
Makes about as much sense as a turkey ham. Or a duck steak. Hen's teeth?
Maybe you could get a little ceramic heat emitter or heat mat and keep it hooked to a thermostat. That is what I do for my reptiles since the temp in my home varies so much.
Our garage stays pretty cold this time of year even when it is hot outside. We live in a valley bottom, in a desert, so we get huge day-to-night temp swings and the garage holds the cool well.
Ice + cold garage and a bucket works fine. You just have to keep an eye on the ice. Cooler makes sense of course, but the thought of all those biohazardy juices infecting a a perfectly good cooler makes me shudder.