  Abundant carbon-chain species have been observed towards lukewarm corinos
L1527, B228, and L483. These carbon-chain species are believed to be
synthesized in the gas phase after CH$_4$ desorbs from the dust grain surface
at the temperature around 30 K. We investigate carbon-chain species formation
in lukewarm corinos using a more rigorous numerical method and advanced surface
chemical models. We use the macroscopic Monte Carlo method in simulations. In
addition to the two-phase model, the basic multiphase model and the new
multiphase models are used for modeling surface chemistry on dust grains. All
volatile species can sublime at their sublimation temperatures in the two-phase
model while most volatile species are frozen in the ice mantle before water ice
sublimes in the basic and the new multiphase models. The new multiphase models
allow more volatile species to sublime at their sublimation temperatures than
the basic multiphase model does. When T $\sim$ 30 K, the abundances of gaseous
CH$_4$ and CO in the two-phase model are the highest while the basic multiphase
model predicts the lowest CO and CH$_4$ abundances among all models. The
abundances of carbon-chain species in the basic and the new multiphase models
are lower than that in the two-phase model when T $\sim$ 30 K because CH$_4$ is
crucial for the synthesis of carbon-chain species. The two-phase model performs
the best to predict carbon-chain species abundances to fit observations while
the basic multiphase model works the worst. The abundances of carbon-chain
species predicted by the new multiphase models agree reasonably well with
observations. The amount of CH$_4$ that can diffuse inside the ice mantle, thus
sublime upon warm-up plays a crucial role in the synthesis of carbon-chain
species in the gas phase. The carbon-chain species observed in lukewarm corinos
may be able to gauge surface chemical models.
