Abstract: 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.