The energy resolution of the conventional way of measuring a small change in a phonon dispersion curve using neutron scattering is restricted by the relatively coarse intrinsic resolution ellipsoid of the neutron triple-axis spectrometer (TAS). By implementing inelastic neutron spin echo on the host TAS using the Larmor precession of the neutron spin, the energy resolution of such measurements can be further improved without reducing the resolution ellipsoid. Measurements of the temperature-dependent phonon energy change are demonstrated using superconducting magnetic Wollaston prisms at the HB-1 instrument of the High-Flux Isotope Reactor at Oak Ridge National Laboratory, and the achievable resolution is <10 µeV.