We present far-infrared (FIR) properties of an extremely luminous infrared galaxy (ELIRG) at zspec = 3.703, WISE J101326.25+611220.1 (WISE 1013+6112). This ELIRG is selected as an IR-bright dust-obscured galaxy based on the photometry from the Sloan Digital Sky Survey and the Wide-field Infrared Survey Explorer (WISE). In order to derive its accurate IR luminosity, we perform follow-up observations at 89 and 154 μm using the High-resolution Airborne Wideband Camera-plus (HAWC+) on board the 2.7 m Stratospheric Observatory For Infrared Astronomy (SOFIA) telescope. We conduct spectral energy distribution (SED) fitting with CIGALE using 15 photometric data (0.4─1300 μm). We successfully pin down FIR SED of WISE 1013+6112 and its IR luminosity is estimated to be LIR = (1.62 ± 0.08) × 1014L☉, making it one of the most luminous IR galaxies in the universe. We determine the dust temperature of WISE 1013+6112 is Tdust = 89 ± 3 K, which is significantly higher than that of other populations such as submillimeter galaxies and FIR-selected galaxies at similar IR luminosities. The resultant dust mass is Mdust = (2.2 ± 0.1) × 108 M☉. This indicates that WISE 1013+6112 has a significant active galactic nucleus and star-forming activity behind a large amount of dust.