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Noise thermometry based on HTS Josephson devices has the potential to provide an absolute technique for the realisation of the temperature scale in the range 4 K-50 K. A resistor connected as a shunt across a YBCO grain boundary junction forms an HTS Josephson Noise Thermometer. We present experimental results and mathematical models for the resistivity of a noble metal film which connects two strips of superconducting YBCO. Accurate temperature measurement requires the resistor to be no more than 1/1000th of the intrinsic junction resistance. This sets an upper limit of 1 m /spl Omega/ for the value of the shunt resistor, including any contact resistance which exists between the metal and YBCO films. Essential aims are firstly to determine the lowest achievable contact resistivity, and secondly to demonstrate a very small variation with current of the contact resistance. A one dimensional model of the current transfer from superconducting to normal films has been used to define the necessary overlap length and also to investigate the possible influence of current dependent proximity effects at the interface. The model is compared with experimental behaviour of two designs of shunt resistance, one a simple rectangular patch configuration and the other a meander line.