FDTD can simulate determinestic devices. When the material property changes with time, you will need to develop your own material model floing the link you referred to. There is no simple script to do this.
You may also simulate the steady state result at each temperature, once you import the heat attribute:
https://optics.ansys.com/hc/en-us/articles/360042833673-Thermally-tuned-waveguide-FDE-
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