Abstract In reduced-order modeling of premixed combustion, a major concern is whether chemistry submodels capture flame characteristics over a broad range of mixture stoichiometries and reactant temperatures. In order to adapt to local temperature level and stoichiometry, models require a suitable parameterization. Post-processing of a large database of adiabatic laminar flame simulations reveals that characteristic temperatures within premixed flames can be collapsed to self-similar structures throughout the lean and ultra-lean premixed regime. The collapse depends on the parameterization, where adiabatic flame temperatures Tad and stoichiometry Φ are identified as natural primary and secondary parameters, respectively. Furthermore, parameterizations of chemical source terms are superior to parameterizations of species profiles, as they allow for a differentiation of chemical processes from transport processes. A comparison of flame characteristics at low and high Tad illustrates that reaction pathways and resulting contributions to the heat release by individual reactions shift according to the temperature level, whereas flames with comparable Tad have similar flame structures that are almost independent of initial temperatures and stoichiometries.