How did they measure the temperature in the reaction?
Very carefully?
The only thing that can measured directly is the distribution and energy of the collision products, as in any particle accelerator experiment. I’m looking at a hard copy of a 2007 Nature article, THE QUEST FOR THE QUARK-GLUON PLASMA, and I see a little diagram that shows the inferred fireball temperature plateauing, as a function of collison energy, at 160Mev. This is E = kT, giving T = E/k = 1.85 Terakelvin.
The news article says they measured temperatures of 4 Terakelvin. As far as I understand it, the 1.85 Tk is the “freeze out” temperature of the fireball, when the quarks recombine into hadrons. The higher temperature is inferred from the total rest and kinetic energy of the collision products. That is, there will be more of them as the fireball cools by converting kinetic energy into mass until it reaches the “freeze out” temperature.