Eventually the cold front catches up with, and merges with, the warm front forming an occluded front. at this stage in the life cycle of an extra-tropical cyclone (known as occlusion, the storm often begins to weaken as the central air pressure begins to:

The extratropical zone reaches an occlusion. This is the time when the storm weakens after the central pressure begins to subside and then slowly becomes colder.  The change lowers the high temperature when the cold front gets over the warm front.

Explanation:

That would be like having a larger output that an input.

Not only are you getting something for nothing, you are getting more than something for nothing.

Our planet just does not work that way. There is one thought experiment that you could perform for yourself that would show you why this isn't possible. It's called Maxwell's Demon.

Pretend that you are in a room that is divided by a wall that does not absorb heat. Pretend also that there is a window in the wall and there is a demon who operates the window.

The demon is programmed so that he opens the window only for the fastest moving molecules. That means that one room would loose heat, and the other would increase its heat content. Your getting something for nothing. You could live in the artificially heated room without spending a dime on heating bills (Of course you might have to feed the demon something).  That thought experiment was developed just as it became understood that temperature is the measurement of a mixture of faster and slower moving molecules.