As /u/Moskau50 correctly explained, there’s a big difference between heat and temperature.
But accelerator beams DO contain a great deal of kinetic energy, which is closely related to thermal energy. For a beam of particles, they are virtually the same thing. In a particle accelerator the beam is typically going at nearly the speed of light, but using particles with mass (unlike light), so there’s quite a bit of energy present. That’s kind of the point of them.
The particles don’t damage the beam tunnel itself because the beam flies through the center of a tube that is in vacuum, held there by very strong electromagnets. The tube must be evacuated so that the beam won’t hit air molecules and lose energy or interact with them. The electromagnets both accelerate the particles and keep them tightly focused near the center of the evacuated tunnel.
Until they meet their target, either a stationary target or a separate beam going the opposite direction. That releases a great deal of energy in the form of light and other particles. If something goes wrong during the process, the beam is typically steered off to something that can absorb the energy without any repercussions. I’ve seen one of these at one of the Stanford Linear Accelerator’s beams and it’s a large block of concrete.
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