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Topological insulators are a class of solids in which the non-trivial inverted bulk band structure gives rise to metallic surface states that are robust against impurity scattering. In three-dimensional (3D) topological insulators, however, the surface Dirac fermions intermix with the conducting bulk, thereby complicating access to the low-energy (Dirac point) charge transport or magnetic response. Here we use differential magnetometry to probe spin rotation in the 3D topological material family (Bi2Se3, Bi2Te3 and Sb2Te3). We report a paramagnetic singularity in the magnetic susceptibility at low magnetic fields that persists up to room temperature, and which we demonstrate to arise from the surfaces of the samples. The singularity is universal to the entire family, largely independent of the bulk carrier density, and consistent with the existence of electronic states near the spin-degenerate Dirac point of the 2D helical metal. The exceptional thermal stability of the signal points to an intrinsic surface cooling process, probably of thermoelectric origin, and establishes a sustainable platform for the singular field-tunable Dirac spin response.