Which element has the highest boiling point of all?

Rhenium, at about 5,900 degrees Celsius - higher than tungsten, which wins on melting point and loses on boiling. Between them they are the two most heat-resistant metals, and rhenium is one of the rarest elements in the crust, at roughly one part per billion.

Nearly all of it goes into jet engines. Nickel superalloys containing a few per cent rhenium make the single-crystal turbine blades in the hot section of a modern engine - components cast as one continuous crystal with no grain boundaries, because grain boundaries are where metal creeps and fails at temperatures above the alloy's own melting point. They survive because they are film-cooled by air bled from the compressor.

That gives it a strange market. Rhenium is recovered mostly as a by-product of copper mining in Chile, supply is small and inelastic, and demand tracks aviation - so the price spiked severalfold in the 2000s and manufacturers spent serious money engineering rhenium out of their alloys. It was also the last stable element to be discovered, in 1925, which makes it the end of a search that had been running since Mendeleev's gaps.