  We present the results from Suzaku observations of the hottest Abell galaxy
cluster A2163 at $z=0.2$. To study the physics of gas heating in cluster
mergers, we investigated hard X-ray emission from the merging cluster A2163,
which hosts the brightest synchrotron radio halo. We analyzed hard X-ray
spectra accumulated from two-pointed Suzaku observations. Non-thermal hard
X-ray emission should result from the inverse Compton (IC) scattering of
relativistic electrons by the CMB photons. To measure this emission, the
dominant thermal emission in the hard X-ray band must be modeled in detail. To
this end, we analyzed the combined broad-band X-ray data of A2163 collected by
Suzaku and XMM-Newton, assuming single- and multi-temperature models for
thermal emission and the power-law model for non-thermal emission. From the
Suzaku data, we detected significant hard X-ray emission from A2163 in the
12-60 keV band at the $28\sigma$ level (or at the $5.5\sigma$ level if a
systematic error is considered). The Suzaku HXD spectrum alone is consistent
with the single-T thermal model of gas temperature $kT=14$ keV. From the XMM
data, we constructed a multi-T model including a very hot ($kT=18$ keV)
component in the NE region. Incorporating the multi-T and the power-law models
into a two-component model with a radio-band photon index, the 12-60 keV energy
flux of non-thermal emission is constrained within $5.3 \pm 0.9 (\pm 3.8)\times
10^{-12}~{\rm erg\, s^{-1} cm^{-2}}$. The 90% upper limit of detected IC
emission is marginal ($< 1.2\times 10^{-11}~{\rm erg\, s^{-1} cm^{-2}}$ in the
12-60 keV). The estimated magnetic field in A2163 is $B > 0.098~{\rm \mu G}$.
While the present results represent a three-fold increase in the accuracy of
the broad band spectral model of A2163, more sensitive hard X-ray observations
are needed to decisively test for the presence of hard X-ray emission due to IC
emission.
