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I would avoid using a spline in data analysis in general. The spline draws smooth curves through arbitrary sets of points but destroys a lot of the information in the points and adds extraneous, meaningless "information". Use it for making things pretty, not for analysis, unless you really think your data should follow a power series (which would be rather ...


Model two consecutive measurements as the real values plus some noise. Call the first measured temperature $T_1$ and the second $T_2$. Call the measured noises $\gamma_1$ and $\gamma_2$, and suppose that they are drawn from a distribution $\Gamma(\gamma)$ and are uncorrelated. The (approximation to the) derivative is $$\text{Derivative} \approx \frac{(T_2 ...

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