The temperature dependence of thermally driven voltage fluctuations of an electrical resistor is described by the dissipation-fluctuation theorem. This fundamental law of statistical physics provides a direct relation between temperature and independently measurable quantities, making the measurement of noise an attractive option for primary thermometry in a wide range of temperatures. However, the realization of such thermometers for the measurement of very low temperatures has often been problematic, preventing this technique from being widely used in low temperature laboratories. We present a novel non-contact approach for Johnson-noise thermometry which uses a commercial dc-SQUID as preamplifier. The noise to be measured is generated by the thermal motion of electrons in a bulk sample of a high purity metal such as gold or copper. These random currents cause fluctuations of magnetic flux in a pickup coil which is connected to the input coil of a current-sensor SQUID. The thermometer is easy to fabricate and rather insensitive to typical sources of parasitic heating. We discuss general design considerations as well as the dependence of the temperature uncertainty upon measurement time. To characterize the thermometer we compared it to a superconducting standard reference device (SRD1000) which represents the temperature scale PLTS-2000. The spectral power density of flux noise was measured as a function of temperature and found to be linear in the investigated range from 6 mK to 4 K.