For example, in a gas at a given temperature, some molecules are more energetic and some molecules are less energetic. The distribution of energy across molecules is called the Maxwell-Boltzmann distribution and has been known, well, since Maxwell. The Maxwell-Boltzmann formula clearly shows that, if you increase the average energy per molecule, the probability of "cold" molecules goes down, not up as you are suggesting.

I am of course not suggesting that a can of gas is a good model for climate, but I want to point out that basic laws of nature push to the opposite direction than the one you are suggesting. Your wider point may well be true, but if so, it depends on more complicated mechanisms than just basic physics.