I agree the calculation probably worked by measuring the kinectic energy of that half-shell by measuring its velocity*thickness directly using pieces of paper.

But I wouldn't count the ideal gas law out (see http://physics.stackexchange.com/questions/43696/will-ideal-...). My guess is that the huge temperatures involved will work in favour of an ideal-gas approximation.

Perhaps the more important thing is that things are happening on very short time-scales, far enough from equilibrium and temperature might not even be well defined.