  We present far-infrared (FIR) properties of an extremely luminous infrared
galaxy (ELIRG) at $z_{\rm spec}$ = 3.703, WISE J101326.25+611220.1
(WISE1013+6112). This ELIRG is selected as an IR-bright dust-obscured galaxy
(DOG) based on the photometry from the Sloan digital sky survey (SDSS) and
wide-field infrared survey explorer (WISE). In order to derive its accurate IR
luminosity, we perform follow-up observations at 89 and 154 $\mu$m 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 $\mu$m). We successfully pin down FIR SED of WISE1013+6112 and
its IR luminosity is estimated to be $L_{\rm IR}$ = (1.62 $\pm$ 0.08) $\times
10^{14}$ $L_{\odot}$, making it one of the most luminous IR galaxies in the
universe. We determine the dust temperature of WISE1013+6112 is $T_{\rm dust}$
= 89 $\pm$ 3 K, which is significantly higher than that of other populations
such as SMGs and FIR-selected galaxies at similar IR luminosities. The
resultant dust mass is $M_{\rm dust}$ = (2.2 $\pm$ 0.1) $\times 10^{8}$
$M_{\odot}$. This indicates that WISE1013+6112 has a significant active
galactic nucleus (AGN) and star-forming activity behind a large amount of dust.
