Look at the appropriate space in which your data would have a normal distribution, or look at the appropriate space in which your data set becomes linear.
This requires knowing the distribution of your experimental data as a prior value.
The correlation coefficient $R$ works best for linearly related data expressable as $y=mx+b$. While $R$ may have some informative value (positive or negative correlation) for non-linearly related variables, it really doesn't have a good clear meaning in non-linear cases.
Takes the logarithm of both sides and get
$$log(a)=b cdot log(T)$$
and see if you can calculate the correlation and do linear regression to find the best fit linear relation between $log(a)$ and $log(T)$. This way, you can see if the correlation coefficient can be informative for you.
But the key thing is in knowing the distribution (or expected distribution) of your data. If it is not normally distributed in the space which you're working in, try to find a transform which moves the data into a space where it has a linear normal Gaussian distribution.
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