Dielectron production in peripheral heavy ion collisions was recently measured by the STAR Collaboration and a significant excess with respect to the hadronic cocktail was observed at low transverse momenta. The excess occurs for pairs with transverse momenta $p_{T}$ $<$ 150 MeV/c and is most prominent in peripheral gold-gold and uranium-uranium collisions. A similar result has been obtained by the ALICE Collaboration in peripheral lead-lead collisions for dileptons from the J/$\Psi$ decay. In peripheral collisions we expect a dominance of hadronic processes so, usually, the dilepton production is studied with models based on hadronic cocktail contributions. However, these models are not able to describe the data, which has motivated the proposition of additional sources of dileptons. An alternative is the dilepton production by photon – photon interactions in heavy ion collisions. In this contribution, we estimate the rapidity and invariant mass distributions for the dielectron and dimuon production in peripheral heavy ion collisions at RHIC and LHC energies considering distinct centralities and different treatments for the nuclear form factor. We also present a procedure to improve the modelling of the dilepton production using the STARLight Monte Carlo, which allows us to derive more realistic predictions.