We present the first semi-analytic radiation transport solutions for the three-temperature (3-T) model: the equations that couple radiation, electron, and ion energy density in a dense plasma. The problem we solve is the 3-T version of the Su-Olson problem considered in a recent radiation diffusion study for verification of a production HEDP code. After linearizing the equations, integral transforms are used to solve the equation, and the inverse transforms are computed numerically after considerable simplication. The results are compared to 2-T transport and 3-T diffusion solutions.