Thermal Index changes

Thermally cycling visible index of refraction (n) is not as easy as changing a thickness with temperature. The index of air is dependent on temperature as well. Since optical power is really dependent on the delta index of refraction, in some cases temperature changes in air need to be considered as well. For visible glasses where the index change with temperature (Dn/DT) is very small, the index change of air HAS to be includedl.

Air index of refraction as a function of temperature
Wavelength, λ, in µm
P is air pressure i Pascals
P0 is Normal pressure (0.101325*1e-6 Pascals)
T is temperature in C°

The Dnair/DT is about -1∙10-6 /C°. Ohara has a reference.

Relationship between relative and absolute index of refraction
Absolute index of refraction is used if your lens is in a vacuum
Relative index of refraction is used if your lens is in air

Schott, an optical glass manufacturer, reports both absolute and relative index of refraction.

Absolute index of refraction
The full nonlinear model of change in index of refraction with change in temperature is
This equation is used by Zemax to model the changes in index of refraction. Embedded in this equation is temperature changes to air's index of refraction.

Infrared index of refraction changes with temperature
The linear component of Dn/DT for infrared materials is usually an order of magnitude larger than visible glasses. Therefore
Dn/DT absolute ~ Dn/DT relative
In addition Dn/DT in the infrared is very difficult to measure and they have huge error bars! So a full nonlinear Dn/DT model is usually not used, but rather a single numeric value is used

=> Infrared materials model index changes with a single Value of Dn/DT instead of a bunch of coefficients.

Reference:

Other visible glass manufactures: