I am assuming you mean 'solids that melt above the temperature of equipment that would hold them'
The answer is: they use the material to hold itself. To melt a volume of material when you don't have a material that can withstand that temp, you simple make a large vat of material and then cool the walls of the vat, letting the material that contacts the vat solidify. You melt the material in the center of the vat. (Maybe via arc heating or induction heating for example)
As for actually measuring the temperature, One of the common ways is using materials we know the melting point of and seeing if they melt or not when placed in/on the other material at its melting point.
And using the spectrum of light emitted by a hot object can be used if you don't know the melting point of anything yet and math can be used to derive the changes of spectrum of light at extremes from temperatures you can more sanely measure.