You posed two distinct questions:
- how is temperature defined as a
- how is temperature measured in these
For the first question, temperature is defined as a thermodynamic quantity relating the change of entropy and the change of internal energy of a system. This is not very intuitive, I agree, but it is THE definition, and it make physicists sure they are talking about the same well-defined quantity.
A somewhat less correct but a much more intuitive definition of temperature is the amount of energy of the chaotic motion per particle. If your particles move chaotically very fast, near the speed of light, so that energy per particle is very large, you temperature is large as well.
As for the second question, physicists measure temperature of heavy-ion collisions indirectly, on the basis of several characteristics they observe in their detectors. The simplest way is by detecting of energetic photons and fitting them to thermal spectrum; another way is by studying the geometry of flow of hundreds of particles produced in the collision and fitting them to some models.