I understand the logic of your example. But, you are measuring one thing and calling it another. Twice as much heat is not half as much cold.

Like having a glass that is half empty. Can you 'remove' the emptiness? No, not without adding something else, and if yes, where did you put the emptiness you removed? If cold exist, what do you measure cold units in and where did they go or come from?
Heat is the energy released from exited molecules. Cold must be energy consumed by the bored ones!

I had a senior engineer that was able to explain this problem very simply in 25 words or less. I am wracking my brain for his explanation (he is in France right now ) My explanation is poor I know.