  Entanglement being a foundational cornerstone of quantum sciences and the
primary resource in quantum information processing, understanding its dynamical
evolution in realistic conditions is essential. Unfortunately, numerous model
studies show that degradation of entanglement from a quantum system's
environment, especially thermal noise, is almost unavoidable. Thus the
appellation `hot entanglement' appears like a contradiction, until Galve et al
[Phys. Rev. Lett. \textbf{105} 180501 (2010)] announced that entanglement can
be kept at high temperatures if one considers a quantum system with
time-dependent coupling between the two parties, each interacting with its
individual bath. With the goal of understanding the sustenance of entanglement
at high temperatures, working with the same model and set up as Galve et al,
namely, parametrically-driven coupled harmonic oscillators interacting with
their own Markovian baths, this work probes into the feasibility of `hot
entanglement' from three aspects listed in the subtitle. Our findings show that
1) hot entanglement functions only in the unstable regimes, 2) instability is a
necessary but not sufficient condition, and 3) the power intake required by the
drive operating in the unstable regime to sustain entanglement increases
exponentially. The last factor indicates that hot entanglement under this
modeling is theoretically untenable and its actual implementation likely
unattainable.
