  Natural hyperbolic two-dimensional systems are a fascinating class of
materials that could open alternative pathways to the manipulation of plasmon
propagation and light-matter interactions. Here, we present a comprehensive
study of the optical response in T$_d\,$-WTe$_2$ by means of density-functional
and many-body perturbation theories. We show how monolayer WTe$_2$ with
in-plane anisotropy sustains hyperbolic plasmon polaritons, which can be tuned
via chemical doping and strain. The latter is able to extend the hyperbolic
regime toward the near infrared with low losses. Moreover, with a moderate
strain, WTe$_2$ can even be switched between elliptic and hyperbolic regimes.
In addition, plasmons in WTe$_2$ are characterized by low losses owing to
electron-phonon scattering, which is responsible for the temperature dependence
of the plasmon line width. Interestingly, the temperature can also be utilized
to tune the in-plane anisotropy of the WTe$_2$ optical response.
