How would they keep the liquid from evaporating? Would they need to enclose it?
They need to find a solid that does not just sublimates when heated in the void.
The problem would be more in choosing a material that has low enough melting point so that making up for the radiative loss to keep it melted wouldn't be a big issue and at the same time vapor losses can be managed. Which is why they propose separate materials for the mirror body and its surface I guess.
Of course it should probably never point at the sun unless they want to melt their sensors.