NGC 6388 reloaded: some like it hot, but not too much

Multiple stellar populations in globular clusters (GCs) are defined and recognized by their chemical signature, with second generation stars showing the effects of nucleosynthesis in the more massive stars of the earliest component formed in the first star formation burst. High temperature H-burning produces the whole pattern of (anti)-correlations among proton-capture elements widely found in GCs. However, where this burning occurred is still debated. Here we introduce new powerful diagnostic plots to detect evidence (if any) of products from proton-capture reactions occurring at very high temperatures. To test these Detectors Of High Temperature (in short DOHT) H-burning plots we show how to put stringent constraints on the temperature range of the first generation polluters that contributed to shape the chemistry of multiple stellar population in the massive bulge GC NGC 6388. Using the largest sample to date (185 stars) of giants with detailed abundance ratios in a single GC (except omega Cen) we may infer that the central temperature of part of the polluters must have been comprised between about 100 and about 150 million Kelvin (MK) if we consider hydrostatic H-burning in the core of massive stars. A much narrower range (110 to 120 MK) is inferred if the polluters can be identified in massive asymptotic giant branch (AGB) stars.