  The double Hawking temperature $T=2T_H$ appears in some approaches to the
Hawking radiation, when the radiation is considered in terms of the quantum
tunneling. We consider the origin of such temperature for the black hole
horizon and also for the cosmological horizon in de Sitter spacetime. In case
the black hole horizon, there are two contributions to the tunneling process of
radiation, each being governed by the temperature $T=2T_H$. These processes are
coherently combined to produce the radiation with the Hawking temperature
$T_H$. This can be traditionally interpreted as the pair creation of two
entangled particles, of which one goes towards the centre of the black hole,
while the other one escapes from the black hole. In case of the cosmological
horizon, the temperature $T=2T_H$ is physical. While the creation of the
entangled pair is described by the Hawking temperature, the de Sitter spacetime
allows for the another process, in which only single (non-entangled) particle
inside the cosmological horizon is created. This process is characterized by
the local temperature $T=2T_H$. Such single particle process takes place also
outside the black hole horizon, but it is exponentially suppressed.
