The use of low-temperature platforms with base temperatures below 1 K is rapidly expanding, for fundamental science, sensitive instrumentation and new technologies of potentially significant commercial impact. Precise measurement of the thermodynamic temperature of these low-temperature platforms is crucial for their operation. In this paper, we describe a practical and user-friendly primary current-sensing noise thermometer (CSNT) for reliable and traceable thermometry and the dissemination of the new kelvin in this temperature regime. Design considerations of the thermometer are discussed, including the optimization of a thermometer for the temperature range to be measured, noise sources and thermalization. We show the procedure taken to make the thermometer primary and contributions to the uncertainty budget. With standard laboratory instrumentation, a relative uncertainty of 1.53% is obtainable. Initial comparison measurements between a primary CSNT and a superconducting reference device traceable to the PLTS-2000 (Provisional Low Temperature Scale of 2000) are presented between 66 and 208 mK, showing good agreement within the k=1 calculated uncertainty.