"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."

Thank you cjameshuff. While that certainly proves me wrong it provides me with intelligent feedback that I can understand rather than "no, you're an idiot" so to speak. I have already emailed CERN with my question and will await their official reply which may take days. In the meantime I will accept that response as valid as I see no error in your logic. My apologies to all for rambling on. I will now go hide in the woods so you can't find me to beat me with sticks.