I repair furnaces when needed. Most of the furnaces I'm responsible
for are about 7.5kW. The muffle will likely have to be replaced along
with the thermocouple (described as being on the bottom).
Thermocouple wires are color coded to identify its type and the
polarity. Here are some links for reading up on thermocouples. Type K
is the most commonly used for this application. Type R and S have
longer operating life but at a much higher cost (Platinum/Rhodium).
They are not interchangeable. The most versatile meters have the
ability to accept all (or most) thermocouple types through program
p.s. The muffle is very brittle material, so use caution when
handling. If the melted metal was on one side of the cylinder, you
could dig it out losing only a small amount of the sidewall. If it's
on the bottom of a cup, any such attempts could break the muffle.