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Here a similar graph where the absolute values of both gradients above the kink is less than 1.

As the derivative move toward -1, the band gap increases (because ln(|x|) has a zero at x=1 with a positive gradient).  In this case the higher temperature curve has a higher band gap.  As temperature decreases the band gap decreases.  The graph shows increasing temperature widen the band gap and move the emitted spectrum towards the ultra-violet band.

If quanta are created with $\cfrac{d\,T}{d\,t}$,  a strong variation in $T$,  $E_{BG}$ will vary through a wide bandwidth and is likely to be white light.