Global warming kinetics
That is a good rule of thumb.  It is based on the Arrhenius equation $$k = A {\operatorname{e}^{\frac{-{E_{\text{act}}}}{RT}}}$$ You'll find that the "temperature doubles every 10 degrees" rule  only applies if the following assumptions are valid


The reaction must obey the Arrhenius equation

it must have an entropic pre-term based on collision probability
the reaction must be an activated process (e.g. it must have an activation energy)



The Arrhenius equation works well for simple unimolecular reactions like the ring opening of cyclobutene to buta-1,3-diene.  

Now you'll need to ask a weather physicist or a meteorologist if weather can be treated as an activated process.  My guess is that the answer is "no", but that's just a guess.  It seems to me that there is no minimum energy required (activation energy) for the rain to fall or for the wind to blow.