In　order　to　improve　the　performance　of　special-gas　infrared　detector,　It　analyses　the　variation　of　temperature　of　the　detector　motivated　by　monochromatic　and　homogeneous　infrared　beam　at　certain　power.　It　proposes　approximate　model　and　establishes　equation　of　heat　conduction　of　absorbing　cell;　Then,　it　gets　the　exact　expression　of　the　variation　of　temperature　everywhere　in　the　absorbing　cell　and　variation　of　average　temperature　through　solution　of　equation.　Discuss　shows　that　responsibility　of　special-gas　infrared　detector　is　linear　with　L,　but　non-linear　with　αλ.　It　establishes　equation　of　heat　conduction　motivated　by　chromatic　infrared　beam　and　proposes　the　solution　of　equation.