Local temperature exponent of a thermonuclear reaction ($d\log \lambda /d\log T=(\eta -2)/3$)

If a charged-particle rate coefficient has $\lambda \propto {\eta }^2{e}^{-\eta }$ with $\eta \propto T^{-1/3}$, its logarithmic temperature derivative is $(\eta -2)/3$. This is a local slope evaluated at fixed composition. It increases as temperature falls, so extrapolating a single power law across a large temperature range can be inaccurate.