The quantitative inversion of present-day downhole thermal indicator information enables (a) assessment of the effective paleoheat flux recorded by thermal indicators, and (b) determination of geological parameters related to the dynamical burial history of sedimentary strata. The logic of the general inversion scheme underlying seven thermal indicators, viz. vitrinite reflectance, sterane, and/or hopane isomers, sterane aromatization, optical rotation,39Ar/40Ar, pollen translucency, and fission scar tracks in apatite is presented, and their capability for resolving paleoheat flux is noted. In a second paper, determination of chemical and physical parameters, as well as several other quantities of geological interest (such as the sizes and erosion times of multiple unconformities, stratigraphic ages, paleo-overpressure, igneous intrusion timing, overthrust timing and frictional heat generation, fault and slump timing, thermal effects due to radioactive layer emplacement, and salt emplacement and dissolution timing) are discussed. Such events impact on both burial and thermal histories of sedimentary layers.