The energies are roughly comparable. A 7 TeV proton has as much kinetic energy as a 1 mg mosquito moving at sqrt(7 TeV/(2*1 mg)) = 0.75 m/s. At this velocity, Newtonian approximations are quite valid...so two mosquitos bumping into each other at 1.5 m/s. The mosquito, however, spreads that energy among roughly 6e20 protons and neutrons, and it doesn't come close to exceeding the binding energy of the mosquitos. Take a flyswatter to a fly and it splatters, do the same to your favored sibling and you'll likely only get the favor returned. Apply 14 TeV to a pair of mosquitos and they bounce, apply it to two protons and they form a tiny fireball of subatomic particles.


At 1 billion collisions/second, there will be a full nanosecond between events. The particles involved were moving at about 30 cm/nanosecond. The debris is not going to hang around for a full nanosecond after a collision at 299792455 m/s. On top of this, the beam at the LHC is composed of multiple bunches, with separate crossing points...the debris of each collision will most likely be well into the detectors by the time the next one occurs at the crossing point it happened in. So once again, yes, the temperature is for each individual collision.