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Gold melts at almost 2000°F (1945°F to be exact; 1063°C) and can be done at home by using a propane torch ($40 at home improvement stores). The propane torch will take a while to get the gold to be hot, then soft, and finally completely melt. Using an oxy-acetelyne torch will speed up the process, but I don't consider that a standard household tool. However, I don't recommend you try this unless you are experienced with this sort of activity.
There have also been some experiments involving conventional (unmodified) microwave ovens and the melting of metals.
<!-- Melting points of various metals Aluminum Al 1220 660 Antimony Sb 1167 630 Beryllium Be 2340 1280 Bismuth Bi 520 271 Cadmium Cd 610 321 Carbon C - - 2.22 Chromium Cr 3430 1890 Cobalt Co 2723 1495 8.90 Copper Cu 1981 1083 8.96 Gold, 24K Pure Au 1945 1063 Iridium Ir 4449 2454 Iron Fe 2802 1539 7.87 Lead Pb 621 327 11.34 Magnesium Mg 1202 650 Manganese Mn 2273 1245 Molybdenum Mo 4760 2625 Nickel Ni 2651 1455 8.90 Osmium Os 4892 2700 22.50 Palladium Pd 2831 1555 Phosphorus P 111 44 Platinum, Pure Pt 3224 1773 15% Irid Plat - 3310 1821 10% Irid Plat - 3250 1788 5% Irid Plat - 3235 1779 Rhodium Rh 3571 1966 Ruthenium Ru 4500 2500 Silicon Si 2605 1430 Silver, Pure Ag 1761 961 Silver, Sterling - 1640 Silver, Coin - 1615 879 Tin Sn 450 232 7.30 Zinc Zn 787 419 7.10 -->
You could likely do it with a MAPP or a turbo torch, but for anything but a bit of wire you would want a small baffle furnace -- you could make an ersatz one one with a few fire bricks (preferably the soft kind), to contain the heat. Or you could use such a furnace with charcoal and forced air. You are essentially making your own equipment such as a jeweler -- or a goldsmith in a primitive culture -- would use.
Keep in mind that you would probably not be trying to melt pure gold, but an alloy which would require a lower temperature than 24K.
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