In this paper the physical and the mathematical model of a three‐temperature plasma is presented. The numerical algorithm used to solve this problem is also described. A special technique has been used to treat very rapid electron‐ion and electron‐radiation energy equipartition rates in inertial fusion plasmas. This model has been incorporated in the one‐dimensional computer codemedusa‐ka. (N. A. Tahir and K. A. Long, ‘‘medusa‐ka: A one‐dimensional computer code for inertial fusion target design,’’ Kernforschungszentrum Karlsruhe Report, KfK‐3454, 1983). Application of this model to study the problem of ignition and burn propagation in reactor‐size inertial fusion targets is also briefly discussed.