We develop a new fluid model of a warm plasma that includes the radiative self-force on each plasma electron. Our approach is a natural generalization of established methods for generating fluid models without radiation reaction. The equilibrium of a magnetized plasma is analysed, and it is shown that the thermal motion is confined to the magnetic field lines. A dispersion relation is deduced for electric waves in a magnetized plasma, and it is shown to agree with our recently established relativistic kinetic theory derived from the Lorentz-Abraham-Dirac equation.