The modulational instability and envelope solitons of ion acoustic waves in an unmagnetized nonthermal electron–positron–ion (epi) plasma are investigated. The ions are taken to be dynamic and warm while electrons and positrons are assumed to be inertialess and hot which follow the kappa (or Generalized Lorentzian) distribution. The Krylov–Bogoliubov–Mitropolsky method is used to derive the nonlinear Schrödinger equation for nonlinear amplitude modulation of ion acoustic waves in nonthermal epi plasmas with warm ions. The dispersive and nonlinear coefficients are obtained for ion acoustic waves in nonthermal epi plasmas which depend on spectral indices of kappa distributed electrons and positrons, ion temperature and positron density. The modulationally stable and unstable regions are studied for a wide range of wave numbers and it is found that the finite ion temperature, positron density and spectral indices of kappa distributed electrons and positrons play a significant role in the formation of bright and dark envelope solitons in nonthermal epi plasmas with adiabatically heated ions. Our findings are applicable to explain some aspects of nonlinear propagation of envelope solitons in astrophysical plasma situations such as neutron stars or pulsars where nonthermal epi plasmas with warm ions can exist (Arons J 2009 Astrophys. Space Sci. Library357 373, Blasi P and Amato E 2011 Astrophys. Space Sci. Proc. pp 623–41, Asif and Saeed 2011 Plasma Phys. Control. Fusion53 095006).