They handle the heat by having an inconceivably small amount of matter at that "temperature". They measure it by looking at the resulting particles and working out how much energy the collision had, and converting between units of energy and temperature.
There are some problems with describing the energy of a particle accelerator as a "temperature", but it makes the article more accessible and understandable, which is surely a good thing.
I don't think there's much of a problem with calling it a temperature. They don't use that term when describing merely one particle scattering off another, they only use it when they are colliding whole nuclei and there are enough particles to observe a thermal distribution. The key part about having a temperature is to have a distribution of modes (e.g. free particle momentum states) and that there is enough mixing around between these modes to generate a thermal distribution.
Should we be making shitty news articles more accessible or understandable, or should we be making the public more literate and intelligent?
At a certain point, dumbing stuff down strips it of all meaning. Our species is going to have to start taking collective responsibility for its collective intelligence if we want a high tech future.
There are some problems with describing the energy of a particle accelerator as a "temperature", but it makes the article more accessible and understandable, which is surely a good thing.