Is it possible to land on sun? The Sun is, of course, quite hot. A space probe built by normal materials probably would melt or burn even it’s still quite far from the Sun.
However, from a theory point of view, is it possible to build a space probe that could land on the Sun?
 A: If, by "land on the sun", you mean "land of the surface of the sun", then you might consider the following from https://solarsystem.nasa.gov/solar-system/sun/in-depth/:

Surface
The surface of the Sun, the photosphere, is a 300-mile-thick
  (500-kilometer-thick) region, from which most of the Sun's radiation
  escapes outward. This is not a solid surface like the surfaces of
  planets. Instead, this is the outer layer of the gassy star.
We see radiation from the photosphere as sunlight when it reaches
  Earth about eight minutes after it leaves the Sun. The temperature of
  the photosphere is about 10,000 degrees Fahrenheit (5,500 degrees
  Celsius).

A: If, by "land on the sun", you mean make a probe that wouldn't melt at solar temperatures, I was going to say "No, of course not. The sun is far too hot." But then I saw New material has higher melting point than any known substance. To my surprise, it stays solid up to 4400 K, 3/4 the temperature of the sun. So I will change my answer to "No. The sun is far too hot."
It is hard to measure the highest boiling points, but Quora says the boiling point of Tungsten is around 5500 or 5600 C, depending on who you ask. Likewise Rhenium boils at 5500 or even 5900 C, again depending on who you ask. Presumably these measurements were made at atmospheric pressure.
The sun is 5778 K = 5504 C. So it would be possible to make a probe that would be just short of boiling at the Sun. So I will change my answer again. "No. The sun is too hot."
Substances can remain liquid or solid at high pressure. According to Nasa, the temperature at the center of Jupiter may be 24,000 C. And yet, the core may be solid. 
As you dive deep into the sun, you can find pressures as high as you like. But the temperature gets high too, much higher than in Jupiter. The sun is gaseous all the way to the core. Nothing we know of could be solid or liquid in the interior of the sun. 
So my final answer is going to be that I don't know of any hard theoretical limit to how high a melting temperature can be. But nothing we know of or even suspect is possible can be solid at the surface of the sun or in its interior. 
And I will add that a probe is more than something that doesn't melt (or boil). It must do something useful. We don't know any way to make electronics or anything else useful under those conditions. 

Edit 2/1/2020 - This XKCD came out since I posted the answer. It seems relevant. https://xkcd.com/2262/
