The impedance and noise of a resistive superconductive quantum interference device (R‐SQUID) have been measured as a function of the dc and rf currents applied to it. The Josephson junction was adjustable so that data were also taken for several values of the junction critical current. The results were compared with the predictions of a resistively shunted junction (RSJ) model which takes into account the influence of the Josephson junction on the impedance and noise. The agreement was found to be quite good and demonstrates that the noise in the circuit is well understood. Use of the R‐SQUID as a noise thermometer below 1 K is assessed in terms of corrections due to the RSJ model. It is demonstrated how the dc and rf currents may be adjusted so that the total noise of the R‐SQUID is reduced to within 0.1% of the Johnson noise generated by the resistor alone. Under these conditions, the R‐SQUID may be used as a noise thermometer to determine thermodynamic temperature to this inaccuracy from 6 to 700 mK.