I know you wrote you'd double checked that the positive terminal is up... Usually the permanent heating should only occur when the NEGATIVE side is up. I wonder what happened, if you swapped your battery the other way.. I DON'T encourage you to do that cause it might be harmful, if you don't take the battery out after some secs - but I still wonder, if you might have mixed up the terminals..?
Don't mean to question your ability to identify the correct terminals! Just trying to make sure, it's all correct..
Good luck - if not, I'm sure Dave will have you covered soon after returning from holidays