If a stony asteroid get so close to it parent star that the siliceous rock would get hot enough to melt, What would happen?
Would the rock turn straight into vapor and form a comet tail line like in icy comets, be a ball liquid rock or something else.
In the hard vacuum of space any material hot enough will quickly evaporate as soon as its molecules are able, thanks to thermal energy, to break the bond with their neighbors.
Add to this the energetic interaction with the stellar wind in such a close proximity to the star, and it's easy to easy that ablative effects will prevail, with the body slowly evaporating into space, the faster the lower its gravity is.
For a reference, Mercury has a tail
Long exposures of our Solar System's innermost planet may reveal something unexpected: a tail. Mercury's thin atmosphere contains small amounts of sodium that glow when excited by light from the Sun. Sunlight also liberates these molecules from Mercury's surface and pushes them away. The yellow glow from sodium, in particular, is relatively bright.
There are rock comets. They are fizzy.
https://astronomy.com/news/2021/09/sodium-may-make-asteroid-phaethon-fizzle
Aptly named after the son of the Sun god in Greek mythology, Phaethon has a 524-day orbit that brings it within just 0.14 astronomical units — where 1 AU is the average distance between the Earth and Sun — of our star, well within Mercury’s orbit. At that distance, the Sun heats the asteroid’s surface to about 1,390 degrees Fahrenheit (750 degrees Celsius). While any water, carbon dioxide, or carbon monoxide ices just under the surface would have evaporated long ago, sodium — an element abundant in asteroids — could be fizzling just under its surface.
Phaeton and the similar "rock comet" Icarus are stony bodies that get very close to the sun. Each of these bodies is thought to have given rise to a cloud of little fragments that rain down on the Earth as meteor showers - The Geminids from Phaeton and the Areitids from Icarus. They get so close to the sun that comety stuff like ice is long gone. There is a thought that boiling sodium inside them might blast off fragments that turn into the meteors which is what you are thinking about - stony stuff melting because of the heat.
I think it is cool that the Geminid meteors were only first observed in the 1800s as opposed to other meteor showers that were seen in ancient times. That would go with them being blasted off their parent more recently.
As L.Dutch mentioned, in principle anything will melt. However, the reason comets develop tails is that they're mostly (water) ice, which melts at a much lower temperature than rock. For a rocky asteroid to melt like a comet, either the star it was orbiting would need to be incredibly bright, or it would need to be very close. Either way, it wouldn't look like a comet - for a regular star, "very close" means "we actually call this 'falling into the star'," while a star bright enough to melt rock at distances over 1 AU would also melt any planets from which you could observe the comet effect (to say nothing of the observers).
The color of lava is red
Your asteroid comes too close is now spiraling quickly into the sun, and you are an inhabitant, standing on the sun's surface looking up, you'd see an asteroid with a long red tail.
Our kind of asteroid 
will look like 
Call it a stone comet ? But it will happen quite fast, you'll probably have to be superman anyway, to get to see it. I'd imagine due to proximity, particles emanating from the sun could distort the diffuse tail,
