The interaction of high-intensity, short-pulse laser radiation with liquids is fundamental to many contemporary technologies. At low laser intensities, the classical model of absorption and heating applies, which assumes a constant absorption coefficient and no dependence on intensity. As the intensity increases, however, many molecules are promoted to excited states, whose absorption properties differ from those of the ground state, and the absorption of the bulk liquid is altered. This phenomenon, called saturable absorption, results in intensity-dependent absorption, heating, and temperature distributions that can deviate significantly from classical absorption. This work investigates the thermal aspects of saturable absorption during laser heating of liquids. A microscopically based model of the radiation absorption and heating processes is presented. Model solutions are discussed and compared with experiment for a contemporary saturable absorbing liquid. Simple engineering criteria and relevant applications are then discussed.