  In previous warm-up chemical models of the low-mass star-forming region
L1527, we investigated the evolution of carbon-chain unsaturated hydrocarbon
species when the envelope temperature is slightly elevated to $T\approx 30$ K.
These models demonstrated that enhanced abundances of such species can be
explained by gas-phase ion-molecule chemistry following the partial sublimation
of methane from grain surfaces. We also concluded that the abundances of
hydrocarbon radicals such as the C$_{\rm n}$H family should be further enhanced
as the temperatures increase to higher values, but this conclusion stood in
contrast with the lack of unambiguous detection of these species toward hot
core and corino sources. Meanwhile, observational surveys have identified
C$_2$H, C$_4$H, CH$_3$CCH, and CH$_3$OH toward hot corinos (especially IRAS
16293-2422) as well as towards L1527, with lower abundances for the carbon
chain radicals and higher abundances for the other two species toward the hot
corinos. In addition, the {\it Herschel Space Telescope} has detected the bare
linear chain C$_3$ in 50 K material surrounding young high-mass stellar
objects. To understand these new results, we revisit previous warm-up models
with an augmented gas-grain network that incorporated reactions from a
gas-phase network that was constructed for use with increased temperature up to
800 K. Some of the newly adopted reactions between carbon-chain species and
abundant H$_2$ possess chemical activation energy barriers. The revised model
results now better reproduce the observed abundances of unsaturated carbon
chains under hot-corino (100 K) conditions and make predictions for the
abundances of bare carbon chains in the 50 K regions observed by Herschel HIFI.
