Analytic and two-dimensional computational solutions for the plasma parameters near a toroidally symmetric limiter are illustrated for the projected parameters of a Tokamak Fusion Core Experiment (TFCX). The temperature near the limiter plate is below 20 eV, except when the density 10 cm inside the limiter contact is 8 × 1013 cm−3 or less and the thermal diffusivity in the edge region is 2 × 104 cm2/s or less. Extrapolation of recent experimental data suggests that neither of these conditions is likely to be met near ignition in TFCX, so a low plasma temperature near the limiter should be considered a likely possibility.