  We consider a mechanical resonator made of diamond, which contains a
nitrogen-vacancy center (NV center) locating at the end of the oscillator. A
second order magnetic gradient is applied and inducing coupling between
mechanical modes and the NV center. By applying proper external magnetic field,
the energy difference between NV center electron spin levels can be tuned to
match the energy difference between two mechanical modes $a$ and $b$. A laser
is used for continuously initializing the NV center electron spin. The mode $a$
with lower frequency is driven by a thermal bath. We find that the temperature
of the mode $b$ is significantly cooled when the heating bath temperature is
increased. We discuss the conditions that quantum regime cooling requires, and
confirm the results by numerical simulation. Finally we give the intuitive
physical explanation on this unusual effect.
