A comprehensive experimental and theoretical study of the low temperature properties of GdCoIn₅ was performed. Specific heat, thermal expansion, magnetization and electrical resistivity were measured in good quality single crystals down to ⁴He temperatures. All the experiments show a second-order-like phase transition at 30 K probably associated with the onset of antiferromagnetic order. The magnetic susceptibility shows a pronounced anisotropy below T_N with an easy magnetic axis perpendicular to the crystallographic ĉ-axis. 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 together with Quantum Monte Carlo calculations of the magnetic contributions show a very good agreement with the experimental data. Comparison between experiment and calculations suggests a significant anharmonic contribution to the specific heat at high temperature (T ≳ 100 K).