Can one use the standard deviation of a variable as a regressor? I am wondering if you could use the standard deviation of a variable as a regressor in an econometrics model? Consider the following hypothetical model:

$$y_{it} = \alpha_0 + \alpha_{1}T_{it} + \alpha_{2}\sigma_{it}^T + u_{it}$$

Where $y$ is the some outcome variable (e.g. crop yields) in country $i$ at time $t$, $T$ is temperature, and $\sigma^T$ is the standard deviation of temperature. Could one interpret $\alpha_2$ in such a way that would indicate how increased volatility in temperature would impact crop yields? 

i.e. testing if countries with greater temperature volatility $\implies$ more severe weather $\implies$ negatively impacts yields

What comes to mind is the use of volatility indices as independent variables, and I wonder if this would lead to a similar interpretation.
By including both regressors, you are effectively trying to find the partial effect of either the temperature level, or variance, on crop yield. That is, the effect of the one, after holding the other constant. Does that approach make sense? Do you need to know the effect of a rise in temperature, for a constant variance in temperature? Or, do you need to know the effect of a change in the deviation in temperature, for a given level in temperature?
The multivariate approach finds those partial effects. The coefficients can be biased if the two variables are correlated with each other—you can test multicollinearity by regressing the one regressor on the other (or, for higher numbers of regressors, one would look at the Variance Inflation Factor).