  We study two different ways to analyze the Hawking evaporation of a
Schwarzschild-de Sitter black hole. The first one uses the standard approach of
surface gravity evaluated at the possible horizons. The second method derives
its results via the Generalized Uncertainty Principle (GUP) which offers a yet
different method to look at the problem. In the case of a Schwarzschild black
hole it is known that this methods affirms the existence of a black hole
remnant (minimal mass $M_{\rm min}$) of the order of Planck mass $m_{\rm pl}$
and a corresponding maximal temperature $T_{\rm max}$ also of the order of
$m_{\rm pl}$. The standard $T(M)$ dispersion relation is, in the GUP
formulation, deformed in the vicinity of Planck length $l_{\rm pl}$ which is
the smallest value the horizon can take. We generalize the uncertainty
principle to Schwarzschild-de Sitter spacetime with the cosmological constant
$\varLambda=1/m_\varLambda^2$ and find a dual relation which, compared to
$M_{\rm min}$ and $T_{\rm max}$, affirms the existence of a maximal mass
$M_{\rm max}$ of the order $(m_{\rm pl}/m_\varLambda)m_{\rm pl}$, minimum
temperature $T_{\rm min} \sim m_\varLambda$. As compared to the standard
approach we find a deformed dispersion relation $T(M)$ close to $l_{\rm pl}$
and in addition at the maximally possible horizon approximately at
$r_\varLambda=1/m_\varLambda$. $T(M)$ agrees with the standard results at
$l_{\rm pl} \ll r \ll r_\varLambda$ (or equivalently at $M_{\rm min} \ll M \ll
M_{\rm max}$).
