  Motivated by recent reports concerning the observation of limited enrichment
in He but excess K in stars of globular clusters, we revisit the H-burning
conditions that lead to the chemical properties of multiple stellar populations
in these systems. In particular, we are interested in correlations of He and K
with other elements, like O, Na, Al, Mg and Si, reported in stars of NGC 2808.
We perform calculations of nucleosynthesis at constant temperature and density,
exploring the temperature range of 25 to 200 10$^6$ K (25 to 200 MK), using a
detailed nuclear reaction network and the most up-to-date nuclear reaction
rates. We find that Mg is the most sensitive "thermometer" of hydrostatic
H-burning conditions, pointing to a temperature range of 70-80 MK for NGC~2808,
while He is a lesser - but not negligible - constraint. K can be produced at
the levels reported for NGC 2808 at temperatures $>$180 MK and Si at T$>$80 MK.
However, in the former temperature range Al and Na are totally destroyed and no
correlation can be obtained, in contrast to the reported observations. None of
the putative polluter sources proposed so far seem to satisfy the ensemble of
nucleosynthesis constraints.
