  A comprehensive experimental and theoretical study of the low temperature
properties of GdCoIn$_5$ was performed. Specific heat, thermal expansion,
magnetization and electrical resistivity were measured in good quality single
crystals down to $^4$He temperatures. All the experiments show a
second-order-like phase transition at 30 K probably associated with the onset
of antiferromagnetic order. Total energy GGA+U calculations indicate a ground
state with magnetic moments localized at the Gd ions and allowed a
determination of the Gd-Gd magnetic interactions. Band structure calculations
of the electron and phonon contributions to the specific heat and Quantum Monte
Carlo calculations of the magnetic contributions to the thermodynamic
quantities reproduce quite well the experimental data.
