A particular type of charged black holes is chosen, based on an action obtained from string theory. This theory predicts the existence of such black holes. Thermodynamic properties of such kinds of black holes are studied. As conjectured earlier, for the dilaton-Maxwell field coupling constant , the behaviors of the thermodynamic parameters (, , , and ) are found to resemble with those of the Reissner–Nordström black hole. The geometrothermodynamics of the aforesaid black hole is studied and the Ricci scalar of the Ruppeiner metric is graphically examined for different values of the parameter . Finally, the parameters as well as the - criticality with different equations for nonzero values of are analyzed. Their deviations from the case of Reissner–Nordström black hole are noted with care. Furthermore, the stability of the black hole is studied by computing the specific heat and analyzing it graphically.