The results of theoretical study of the temperature dependence of a long-wave range fundamental absorption edge in flat nanoheterostructures with a single quantum well (nanofilms) are adduced. The quantum well is assumed to be rectangular, of finite depth, and with unstrained heterojunctions as the nanofilm surface. Energies of electrons, holes, and excitons have been calculated within the framework of the effective mass model using the Green functions techniques, with account of their interaction with polar optical phonons confined within a quantum well. Numerical calculations are performed for nanofilms β-CdS/β-HgS/β-CdS and Al0.3Ga0.7As/GaAs/Al0.3Ga0.7As. It is shown that interaction with optical phonons causes a long-wave shift of the threshold frequency of the fundamental absorption band and a shift of exciton peaks by hundreds of Å for the first mentioned nanofilm and by dozens of Å for the second one, which is characterized by lower magnitudes of the constants of the electron-phonon coupling. The shift magnitude, as well as the height and half-width of the exciton absorption band, changes when the temperature exceeds 80 and 100 K, respectively.