Thermalisation of particle This is most likely an extremely basic question, a question of terminology,
When people discuss a particle being thermalised do they mean the particle is brought into thermal equilibrium?
 A: Particles at a given temperature have a distribution of energies and on average there is no transfer of kinetic energy between the particles when they collide.  They are in an equilibrium state.
Imagine a particle with a lot of kinetic energy ("hot" particle) being placed with the other particles.
This will result in collisions/interaction between the hot particle and the other particles which will result in a net transfer of kinetic energy from the hot particle to the other particles.
Eventually the hot particle will on average not transfer kinetic energy to the other particles and so it will have been thermalised.
Due to the addition of the hot particle the final state will be a group of particles with a slightly higher average kinetic energy (temperature) than before the introduction of the hot particle.
The particles are now in a new equilibrium state.
A good example of thermalisation is in a nuclear reactor.
The neutrons produced from the fission process have a very high kinetic energy (fast neutrons) and are thus less likely to be captured by uranium nuclei than low energy neutrons (thermal neutrons).
In the reactor there is a moderator whose purpose is to reduce the kinetic energy of the emitted neutrons by collision with the atoms of the moderator which on average have much less kinetic energy than the neutrons.
The neutrons after having been slowed down have energies ~0.03 eV having started out with energies of ~2 MeV.
A: Thermalisation is a somewhat vague term meaning the particle kinetic energy is reduced (or increased) to be of order $kT$.
If a particle is in thermal equilibrium with surroundings at a temperature $T$ then each of its degrees of freedom would have an energy of $\tfrac{1}{2}kT$. For an elementary particle the only degrees of freedom are the three translational degrees of freedom, so the average particle energy will be around $\tfrac{3}{2}kT$.
