  We report the temperature dependence of the upper critical fields
$\mu_0H_{c2}(T)$ of the high temperature superconductor H$_3$S under applied
pressures of 155 and 160 GPa through the electrical resistance transition
observed under DC and pulsed magnetic fields up to 65 T, a record high
combination of fields and pressures. We find that $H_{c2}(T)$ generally follows
the Werthamer, Helfand and Hohenberg (WHH) formalism at low fields, albeit with
noticeable deviations upon approaching our experimental limit of $\mu_0H = 65$
T. In fact, $H_{c2}(T)$ displays a remarkably linear dependence on temperature
over an extended temperature range also found in multigap or in
strongly-coupled superconductors. The best fit of $H_{c2}(T)$ to the WHH
formula yields a negligible value for the Maki parameter $\alpha$ and for
spin-orbit scattering constant $\lambda_{\text{SO}}$. However, its behavior is
relatively well-described by a model based on strong coupling superconductivity
with a coupling constant $\lambda \sim 2$. Therefore, we conclude that H$_3$S
behaves as a strong-coupled orbital-limited superconductor over the entire
range of temperatures and fields used for our measurements.
