Radiative recombination (inverse photoionization) is believed to be well understood since the beginning of quantum mechanics. Still, modern experiments consistently reveal excess recombination rates at very low electron-ion center-of-mass energies. In a detailed study on recombination of F and C ions with magnetically guided electrons we explored the yet unexplained rate enhancement, its dependence on the magnetic field B, the electron density n(e), and the beam temperatures T-perpendicular to and T-parallel to. The excess scales as T-perpendicular to(-1/2) and, surprisingly, as T-parallel to(-1/2), increases strongly with B, and is insensitive to n(e). This puts strong constraints on explanations of the enhancement.