The event-by-event p(T) fluctuations in proton-proton and central Pb-Pb col
lisions, which have been experimentally studied by means of the so-called P
hi measure, are analyzed. The contribution due to the correlation that coup
les the average p(T) to the event multiplicity is computed. The correlation
appears to be far too weak to explain the preliminary experimental value o
f Phi (p(T)) in p-p interactions. The significance of the result is discuss
ed.