The upgrade of its ion cyclotron resonance (ICRH) and lower hybrid current drive (LHCD) heating systems makes the Tore Supra (TS) tokamak particularly well suited to address the physics and technology of high-power and steady-state plasma–surface interactions. High radio frequency (RF) heating powers have been successfully applied up to 12.2 MW coupled to the plasma, in which about 7.85 MW flows through the scrape-off layer. Thermal calculation based on thermography measurements gives the heat flux density distribution on the TS toroidal limiter located at the bottom of the machine. The target heat flux densities are divided by the incidence angle of the field lines with the surface and mapped to the magnetic flux surface to evaluate the power flowing in the scrape-off layer (SOL). The power profile shows a narrow component near the last closed flux surface and a wide component in the rest of the SOL. The narrow component is attributed to significant cross-field heat flux density around the plasma contact point, about 0.8% of the parallel heat flux density in the SOL, when incident angles are nearly tangential to the surface. The wide component is used to derive the experimental heat flux decay length (λq) and parallel heat flux in the SOL. The power widths are measured for a series of 1 MA/3.8 T discharges involving a scan of RF injected power 3.5 ⩽ Ptot ⩽ 12.2 MW. Independently of the heating power, we measured λq,OMP = 14.5 ± 1.5 mm at the outer mid-plane and parallel heat flux in the SOL in the range . TS values obtained with L-mode limiter plasmas are broader than those derived from L-mode divertor plasmas, confirming earlier results obtained with an ohmically heated plasma leaning on the inboard wall of TS.