  We demonstrate that the existing neutron-star cooling data can be
appropriately described within "the nuclear medium cooling scenario" including
hyperons under the assumption that different sources have different masses. We
use a stiff equation of state of the relativistic mean-field model MKVORH$\phi$
with hadron effective couplings and masses dependent on the scalar field. It
fulfills a large number of experimental constraints on the equation of state of
the nuclear matter including the $2\,M_{\odot}$ lower bound for the maximum
predicted neutron-star mass and the constraint for the pressure from the
heavy-ion particle flow. We select appropriate $^1S_0$ proton and $\Lambda$
hyperon pairing gap profiles from those exploited in the literature and allow
for a variation of the effective pion gap controlling the efficiency of the
medium modified Urca process. The $^3P_2$ neutron pairing gap is assumed to be
negligibly small in our scenario. The possibility of the pion, kaon and charged
$\rho$-meson condensations is for simplicity suppressed. The resulting cooling
curves prove to be sensitive to the value and the density dependence of the pp
pairing gap and rather insensitive to the values of the $^1S_0$ neutron pairing
gaps.
