Q:

Can a planet be so near to a star that anything flying above a certain height would start melting or combusting?

Its a very wip idea: I have a star that's not very hot, and the planet is very close to it. Can the planet be so close to the star to be livable on the surface, but flying at cruise height(10 km) would mean melting or burning. And if yes? How close? And how hot should it be?
The sizes of the sun is roughly half of the sun, the same applies to the planet (half the size of earth). If any information is needed just ask.
Since this is probably impossible in real sience, let's not be stopped from that. Its a universe with huge wormholes and object faster than light, so bending the physics a little more won't hurt. The size of both object can be changed too if needed

A:

I understand you are not talking about earth but about your world.  You could set your planet up this way by covering it with low thick clouds with a very high cloud albedo.
From https://en.wikipedia.org/wiki/Cloud_albedo

Studies have shown that cloud liquid water path varies with changing
  cloud droplet size, which may alter the behavior of clouds and their
  albedo.[6] The variations of the albedo of typical clouds in the
  atmosphere are dominated by the column amount of liquid water and ice
  in the cloud.[2] Cloud albedo varies from less than 10% to more than
  90% and depends on drop sizes, liquid water or ice content, thickness
  of the cloud, and the sun's zenith angle. The smaller the drops and
  the greater the liquid water content, the greater the cloud albedo, if
  all other factors are the same.
Addition of cloud nuclei by pollution can lead to an increase in solar
  radiation reflected by clouds.[7] Increasing aerosol concentration and
  aerosol density increases cloud droplet concentration, decreases cloud
  droplet size, and increases cloud albedo.[2][6] In macrophysically
  identical clouds, a cloud with few larger drops will have a lower
  albedo than a cloud with more smaller drops.

So thick, low clouds with lots of particulates.  Beijing world?  Wet, low, bright (when seen from above) clouds.  Seattle world?
In any case, if you have clouds with albedo of 90% covering the ground, you can have it be substantially hotter above at cruising altitude - both from unintercepted solar radiation coming from the sun as well as 90% of that amount of radiation being reflected up from below.  

A:

Can the planet be so close to the star to be livable on the surface, but flying at cruise height(10 km) would mean melting or burning

Not through nearness to the sun, for a number of reasons:

that close, it would be within the star's corona
solar flares and magnetic reconnections would blow the atmosphere off
attrition with the solar atmosphere would send the planet spiraling to its doom in a few years
thermal equilibrium would mean the planet itself gets melted

But @Will has the right of it: you can have most of the radiation being reflected back by a cloud layer. Playing with physics, you can imagine a sort of "liquid" atmosphere or a layer of gases with so low a resistivity as to behave like a metallic mirror, reflecting 99% of the incoming radiation.
In our Universe, there are no life-sustaining dense liquids; in your Universe, there might be, and they could form the planet's atmosphere (around 5,000 times denser than Earth's, and much less thick). So you could have a whole world completely covered in "liquid" (except that its denser inhabitants call it "air"); to make things worse, above the liquid, a thin layer of molten metal such as gallium ensures a reflectivity of 99.5%. Only a half of one percent of the incoming radiation ever makes it to the surface. On the night side, the metal oxidizes and becomes black, re-radiating heat into space.
Flying over this "shield" would expose you to a radiation level four hundred times surface normal, and possibly also to a very different chemical composition of the "atmosphere", causing immediate ignition. A hell of a myth of Icarus.

A:

A different solution:
Have your planet be tidally locked to the star (so that one side always faces the sun) and much closer to the star than Earth equivalent.  The population lives in the twilight habitable lands between the burning hot side and the freezing shadow side.
Any aircraft flying in the twilight region rising above a certain altitude would pass outside of the shadow of the planet and be exposed to the full force of the nearby star.  Kind of like watching a sunrise on Mercury.

