  Hawking radiation is an important quantum phenomenon of black hole, which is
closely related to the existence of event horizon of black hole. The
cosmological event horizon of de Sitter space is also of the Hawking radiation
with thermal spectrum. By use of the tunneling approach, we show that there is
indeed a Hawking radiation with temperature, $T=1/2\pi \tilde r_A$, for locally
defined apparent horizon of a Friedmann-Robertson-Walker universe with any
spatial curvature, where $\tilde r_A$ is the apparent horizon radius. Thus we
fill in the gap existing in the literature investigating the relation between
the first law of thermodynamics and Friedmann equations, there the apparent
horizon is assumed to have such a temperature without any proof. In addition,
we stress the implication of the Hawking temperature associated with the
apparent horizon.
