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Maybe a Differential Thermal Analysis/Thermomechanical Analysia? I suspect gold and tungsten have different behaviours when heated, and that should tell both apart.

https://en.wikipedia.org/wiki/Differential_thermal_analysis https://en.wikipedia.org/wiki/Thermomechanical_analysis

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They have different magnetic susceptibilities. Gold is diamagnetic (repelled by magnetism); tungsten is paramagnetic (attracted). A strong magnetic field (neodymium magnets) and sensitive scales can tell them apart. I built a small rig a few years ago with parts from Aliexpress that worked for coins and for bars it's just scaling it up.

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