We use the Karl G. Jansky Very Large Array ( VLA ) to conduct a high-sensitivity survey of neutral hydrogen ( H i ) absorption in the Milky Way . In combination with corresponding H i emission spectra obtained mostly with the Arecibo Observatory , we detect a widespread warm neutral medium ( WNM ) component with excitation temperature \left < T _ { s } \right > = 7200 ^ { +1800 } _ { -1200 } K ( 68 % confidence ) . This temperature lies above theoretical predictions based on collisional excitation alone , implying that Ly- \alpha scattering , the most probable additional source of excitation , is more important in the interstellar medium ( ISM ) than previously assumed . Our results demonstrate that H i absorption can be used to constrain the Ly- \alpha radiation field , a critical quantity for studying the energy balance in the ISM and intergalactic medium yet notoriously difficult to model because of its complicated radiative transfer , in and around galaxies nearby and at high redshift .