depends on the quality of the coal, you could possibly try and make your own coke, fill the pan with coal, put lid on pan and cook the coal on an open fire, lid must be loose to allow all the gases to escape. but you should (i have never tried this) end up with coke and that should burn at the temperatures you need. Coke is just coal with the impurities removed,
of course, if you have enough gold to melt, then buy a proper furnace (type of thing for aluminium) you clearly have the funds to affoard it.
But yes, I also love the DIY approach - I made something similar years ago out of an old air compressor cylinder, I used anthracite (smokeless coal) and an old hairdrier to blow air into the bottom, it got seriously hot. I was heat treating old carbon rich files so as I could turn them into wood turning chisels - had to 'normalise', them first, annealing was probably better, then fashion them into chisels, then re-harden and then temper - all fascinating stuff