  The observed anomalous steady decrease in surface temperature of the
supernova remnant Cassiopeia A (Cas A), which was reported about ten years ago,
has generated much debate. Several exotic cooling scenarios have been proposed
using non-standard assumptions about the physics and evolution of this neutron
star (NS). At present, significant corrections have been made to the
observational data, which make it possible to numerically simulate the Cas A NS
cooling process in the framework of the scenario of minimal neutrino cooling.
If there is an additional source of cooling, such as axion emission, the
steepness of the Cas A NS surface temperature drop will increase with the
growth of the axion-nucleon interaction strength. This makes it possible to
limit the minimum value of the axion decay constant $f_a$ using the condition
that the NS surface temperature should be within the 99% confidence interval
obtained from the observational data. Two types of axion models are considered:
the Kim-Shifman-Weinstein-Zakharov -- KSVZ model and the
Dean-Fischler-Srednitsky-Zhitnitsky --DFSZ model. The above criterion gives a
lower limit on the axion decay constant, $f_a>3\times 10^7$ GeV and
$f_a>4.5\times 10^8$ GeV for KSVZ and DFSZ axions, respectively.
