Synthesis of hafnium carbide via one-step selective laser reaction pyrolysis

In air, they would burn, like a furnace made of graphite also does.

So for reaching such high temperatures, you need not only a refractory material like hafnium carbide for the furnace, but you need also to keep all hot parts in a protective inert gas, e.g. argon, and there is also the condition that whatever you want to melt in the furnace must not react chemically with carbides at such high temperatures.

For example, for melting many kinds of oxides the best that you can do is to use an iridium furnace, whose melting temperature is far lower than that of hafnium carbide or graphite, but it does not react chemically with the oxide of any metal more reactive than iridium (which covers most metals). For some oxides a molybdenum furnace is good enough.

The suitable material for a furnace depends on what you want to melt. Furnaces made of carbides or of graphite are normally not suitable for iron and related metals, which have high affinity for carbon, so they could dissolve the furnace at very high temperatures. A furnace made of magnesia (magnesium oxide) is likely to be the furnace that can reach the highest temperatures when in contact with such metals.