Focusing the beam in this case may be difficult even in principle. The radiation is initially incoherent. The radiation is initially not uncollimated. There are several laws of physics that would prevent this chaotic radiation from being collimated over large distances.
Let us start with the laws thermodynamics. Initially, the radiation is incoherent and nearly isotropic. There are many degrees of freedom in this radiation. Therefore, the radiation has a large entropy content. When you collimate the beam, you are reducing the degrees of freedom. Therefore, in order to collimate the radiation completely you would have to destroy entropy. Therefore, there is no way to collimate a beam into a small area. The second law of thermodynamics places a limit on how tightly one can collimate a beam.
It turns out that even if you collimated the beam, you would need a large area to dissipate the energy. The thermal radiation would have to be collected over a large area before you collimated it. Otherwise, you would violate the second law of thermodynamics.
Now let us look at the problem from the point of imaging optics. The radiation from the hot object is incoherent. Therefore, the light coming from the hot object acts like an image. The imaging laws for lenses applies to all curved mirrors and curved lenses that are used to collimate the light. According to the laws of lenses, the image can't be shrunk to nothing. All you could do is make a smaller real image. Again, there is only a portion of the thermal radiation that can go into making a smaller image.
You could do this in terms of diffraction. The thermal radiation has a black body spectrum. Therefore, it has a spread of wavelengths. Therefore, diffraction effects prevent one from focusing or collimating the beam. There is an uncertainty relation here that may help.
A young man that I knew suggested making a death ray out of a flashlight and a large array of lenses. He suggested taking a large number of lenses to focus and collimate the beam from the flash light into a very small area. The beam would remain in a small area over a long distance. Within that area, material would be vaporized. One could then cut tanks and airplanes to pieces using this flashlight. I explained that it would not work due to the Second Law of Thermodynamics. The beam would spread out two quickly from the focal point.
He then asked me whether I ever tried it. The answer, of course, was yes. In the course of my work, I have often had a needed for a tightly focuses and tightly collimated beam of thermal radiation. I had tried many times to use lenses (refractive and reflective) to focus such radiation. It wasn't until I did some calculations using the Second Law that I gave up.
I have often wondered what would have happened if I was wrong. Suppose this young man had decided not to listen. Suppose three were a team of rebellious teenagers who didn't listen to mainstream scientists. They went ahead and made these death rays out of flashlight batteries.
Each one could split mountains in half on two Ever Ready batteries! Each one could destroy cities using one single candle!
They would also be able to cure the worlds energy woes. Using such an array of lenses, they could make perpetual motion machines that destroy entropy.
Maybe that would make a good science fiction story. Someone comes up with that hidden combination of lenses that break the Second Law of Thermodynamics.