  We study the $(d+2)$-dimensional Hyperscaling Violating (HV) geometries in
the presence of both a finite temperature $T$ and a UV cutoff $r_c$. This
gravitational system is conjectured to be dual to $T\bar{T}$ like deformed HV
QFTs. We consider the representative quantum entanglement quantity in
holography, i.e. the entanglement entropy $S(A)$, and perform a complete
analysis in all possible parameter ranges of the hyperscaling violation
exponent $\theta$ and the critical dynamical exponent $z$ to study the effect
of the temperature and the cutoff. We find that the temperature has a universal
effect independent of the parameters: it enhances $S(A)$ in the small cutoff
limit, while it is irrelevant in the large cutoff limit. For the cutoff effect,
we find that the cutoff monotonically suppresses $S(A)$ where its behavior
depends on the parameter range. As an application of the finite temperature
analysis, we study the first law of entanglement entropy,
$S_{T}-S_{T=0}\sim\ell^{\lambda}$, in the small subsystem size $\ell$ limit. We
find that $\lambda$ interpolates between $\lambda=1+z$ in the small cutoff and
$\lambda=3$ in the large cutoff, independent of the parameter range. We also
provide the analytic holographic result at $z=d-\theta$ and discuss its
possibility of comparison with the field theoretic result.
