Military infrared systems generally must exhibit stable optical performance over a wide operating temperature range. We present a model for the first-order optical design of radial gradient-index systems, based on a form of the thermo-optic glass coefficient adapted to inhomogeneous material combinations. We find that GRIN components can significantly reduce the optical power balance of athermal, achromatic systems, which introduces the scope for a new class of broadband infrared imaging solutions. This novel first-order modelling technique is used to generate a starting point for optimisation of a SWIR/LWIR multispectral optical design.