Your analysis is excellent ...
You've convinced me that it would take a significant time to cool. I forgot how tiny the S-B constant was, so that offsets the temp^4. All I was thinking of was the temp^4 part.
I also did a double take on the heat capacity, then I looked again and realized you're using joules and not calories. I've been programmed to use calories for heat calculations the last three years!
You have shamed me into submission, Mr. S.
I was actually surprised it would cool that slowly as well. I went through the math twice.