How does heat radiate away from concave surface? If I shine a light on a parabolic mirror parallel to optic axis, all of the rays will be reflected through its focal point. What happens if I heat it? Is heat going to be radiated through the focal point or will it be spread in all directions?
Edit: The question is about direction of heat emissions. Is heat emitted in only one direction, perpendicular to the surface or in all directions from each of the points on the mirror? Mirror is heated internally, it is not reflecting anything.
 A: You seem to be thinking of a macroscopic mirror, one whose dimensions are much larger than the wavelength of the emitted black-body radiation. Also, the mirror appears to be smooth enough to have a well-defined focal point. In other words, it is locally flat (almost) everywhere.
In this simple model, the thermal radiation that's locally emitted is going to be uniformly distributed - there's simply no preferred direction. But on a non-local scale, some of the emitted photons may hit the mirror. In turn, some of these may be absorbed, while others are reflected.
Now note that the photons that are absorbed again do not cause local heating. The reason is fairly simple once you realize that light paths are reversible. If a thermal photon emitted at point A hits point B, then thermal photons emitted from B can also travel back to A.
Still, the photons that are emitted at A and reflected at point B will be subtracted from the original uniform distribution, and have a new direction dependent on the angle between the vector AB and the surface normal at point B. For the effects of a single reflection, you'd have to double integrate this over all points A and all points B visible from points A. And of course a photon could be reflected more than once - consider a concave mirror that's shaped like a tube - that's quite similar tp a glass fiber.
A: 
Is heat emitted in only one direction, perpendicular to the surface or in all directions from each of the points on the mirror?

Thermal radiation is emitted in all directions at each point on the surface. It is not coherent in either frequency or direction. That said, a good reflector like a mirror will not be a particularly good emitter of thermal radiation. It will emit substantially less than a black body at the same temperature. Some of that emitted radiation will reflect off the concave surface, at odd but non-random angles.
A: Heat as part of the electromagnetic spectrum, in terms of energy, as light or infrared rays, acts as a waves (classically). Say, the heat is in the infrared spectrum instead of light. If it is directed towards the concave mirror, it will still reflect to the focal point, the same as light, but you would not be able to see it without an infrared camera.
