We report an inelastic neutron scattering study on the low-energy magnetic excitations of Ba₂CoGe₂O₇ single crystal under applied magnetic fields for several fixed temperatures. We have observed a sizable spin gap of ≈ 0.105 meV for the acoustic mode at 2.2K under zero magnetic field whereas, no changes in energy of the optical modes at magnetic zone center are observed under varying temperature. However, spin gap of the acoustic mode at finite fields also evolves under varying temperature and the gap energy decreases with increasing temperature. Interestingly, the difference between the spin gap at 2.2 and 4.6K is about ≈ 0.025 meV for all the applied fields of 0.35, 1 and 5 T. Our results enlighten the discussion in details on understanding the origin of the spin gap in Ba₂CoGe₂O₇.