The nonlinear interaction between large-amplitude electromagnetic waves and electron-acoustic (EA) waves in a two-electron-temperature plasma is considered, taking into account the combined effects of the radiation pressure and the thermal force involving the differential Joule heating of the electrons caused by the electromagnetic waves. By employing a fluid approach, we derive a system of coupled equations for the electromagnetic waves and the EA waves; the latter are nonlinearly driven by the radiation and thermal forces. We have carried out a normal mode analysis of our nonlinearly coupled equations, and have derived a general dispersion relation that is useful for studying different types of parametric instabilities. A new class of modulational instability in the collision-dominated regime is identified. The implications for space and laboratory plasmas are pointed out.