The superconducting transition temperature of more than 30 thin-film tungsten samples was measured using a dilution refrigerator. The samples were fabricated using a 99.999% pure tungsten target and a dc magnetron sputtering system. Individual films were then doped with metal impurity ions using an accurate ion implantation technique. The effect of the metal–ion doping on the superconducting transition temperature was measured for samples with superconducting transitions in the range of 40–150 mK. Magnetic dopant species including Ni, Co, and Fe resulted in suppressed values of the tungsten Tc. The suppression was linear with increasing dopant concentration, for concentrations up to tens of ppm. For higher concentrations of magnetic atoms, the data are consistent with the Abrikosov–Gor'kov theory [Soviet Physics JETP 12, 1243 (1961)] modified by antiferromagnetic impurity–impurity interactions. By contrast, tungsten films implanted with Mg or Cr showed little change in Tc after doping. In this article, we present data from cryogenic experiments on these films. We also present x-ray diffraction (XRD) spectra for a subset of the films. Our XRD data confirm that the observed suppression in Tc for the magnetically doped samples is not due to any structural changes (e.g., lattice distortion or damage) induced by the implantation process.