  Nonclassicality conditions for an oscillator-like system interacting with a
hot thermal bath are considered. Nonclassical properties of quantum states can
be conserved up to a certain temperature threshold only. In this case,
affection of the thermal noise can be compensated via transformation of an
observable, which tests the nonclassicality (witness function). Possibilities
for experimental implementations based on unbalanced homodyning are discussed.
At the same time, we demonstrate that the scheme based on balanced homodyning
cannot be improved for noisy states with proposed technique and should be
applied directly.
