A comparative study of the temperature dependences of the photoluminescence (PL) of aqueous CdSe and silver-indium-sulfide (AIS) nanocrystals (NCs) in a broad range of 10-310 K is reported. Gelatin-incorporated CdSe (and core/shell CdSe/ZnS) NCs reveal both direct (excitonic) and trap-state-mediated PL components with different temperature dependences of the PL band maximum and spectral width. Glutathione-capped AIS (and core/shell AIS/ZnS) NCs emit a single broad PL band resembling the trap-related PL of CdSe NCs but showing nevertheless a temperature PL dependence typical for excitonic PL. In combination with previously reported results, these special features allow the PL emission of ternary AIS (AIS/ZnS) NCs to be explained based on the recombination of self-trapped excitons.