In the Large Hadron Collider (LHC), protons are accelerated to very high energies but their temperature, in the conventional sense, is not well-defined. Temperature is a measure of the average kinetic energy of particles, typically related to their random thermal motion.
In the LHC, protons are accelerated to energies of several tera-electron volts (TeV), which corresponds to speeds very close to the speed of light. At these energies, the concept of temperature as a measure of thermal motion doesn't apply directly. The protons in the LHC are not in a thermal equilibrium or a thermalized state, as would be the case in a system with a well-defined temperature.
Instead, the protons in the LHC are focused into extremely narrow beams and are kept in a high-energy state. Their motion is predominantly determined by the electromagnetic fields that accelerate and guide them around the collider ring. The focus is on colliding the protons at specific interaction points, where their high energies are used to create and study high-energy particle collisions.
Therefore, while the protons in the LHC have extremely high energies, it is more appropriate to describe their state in terms of their momentum and energy rather than a temperature associated with thermal motion.