You don’t need to apologize for the need to learn something. I had one customer who remarked – “I’ve been working with gratings all my career and never seen that effect before – well, you never stop learning until you are dead”. How True!!
There is no direct connection between temperature and wavelength. In the sensors section of OptiGrating, the temperature influences the spectrum though material properties thermo-optic and thermal expansion coefficients. The thermo-optic effect is the temperature changing the refractive index of the material. The thermal expansion coefficient is the strain (expansion, displacement) caused by heat. The expansion changes the grating period and optical gratings are very sensitive to period. The author of OptiGrating thought that sometimes the heat might not be applied uniformly over the whole length of the grating. It might be applied in some distribution, hotter in some places than others, and therefore it would be a non-uniform grating. One would have to calculate the spectrum in steps, as done for apodized, chirped or otherwise nonuniform gratings.