  We present a 155ks NuSTAR observation of the $z\sim2$ hot dust-obscured
galaxy (hot DOG) W1835+4355. We extracted spectra from the two NuSTAR detectors
and analyzed them jointly with the archival XMM PN and MOS spectra. We
performed a spectroscopic analysis based on both phenomenological and
physically motivated models employing toroidal and spherical geometry for the
obscurer. In all the modelings, the source exhibits a Compton-thick column
density $N_{\rm H} \gtrsim 10^{24}$ cm$^{-2}$, a 2-10 keV luminosity
$L_{2-10}\approx2\times10^{45}$ erg s$^{-1}$ , and a prominent soft excess
($\sim5-10$ % of the primary radiative output), which translates into a
luminosity $\sim10^{44}$ erg s$^{-1}$. We modeled the spectral energy
distribution from 1.6 to 850 $\mu m$ using a clumpy two-phase dusty torus model
plus a modified blackbody to account for emission powered by star formation in
the far-infrared. We employed several geometrical configurations consistent
with those applied in the X-ray analysis. In all cases we obtained a bolometric
luminosity $L_{\rm bol}\approx3-5\times10^{47}$ erg s$^{-1}$, which confirms
the hyperluminous nature of this active galactic nucleus. Finally, we estimate
a prodigious star formation rate of $\sim$3000 $M_{\odot}\,yr^{-1}$, which is
consistent with the rates inferred for $z\approx2-4$ hyperluminous type I
quasars. The heavily obscured nature, together with $L_{\rm bol}$, the ratio of
X-ray to mid-infrared luminosity, the rest-frame optical morphology, and the
host star formation rate are indicative of its evolutionary stage. We can
interpret this as a late-stage merger event in the transitional,
dust-enshrouded, evolutionary phase eventually leading to an optically bright
AGN.
