  We present a detailed study of a Brownian particle driven by Carnot-type
refrigerating protocol operating between two thermal baths. Both the
underdamped as well as the overdamped limits are investigated. The particle is
in a harmonic potential with time-periodic strength that drives the particle
cyclically between the baths. Each cycle consists of two isothermal steps at
different temperatures and two adiabatic steps connecting them. Besides working
as a stochastic refrigerator, it is shown analytically that in the quasistatic
regime the system can also act as stochastic heater, depending on the bath
temperatures. Interestingly, in non-quasistatic regime, our system can even
work as a stochastic heat engine for certain range of cycle time and bath
temperatures. We show that the operation of this engine is not reliable. The
fluctuations of stochastic efficiency/coefficient of performance (COP) dominate
their mean values. Their distributions show power law tails, however the
exponents are not universal. Our study reveals that microscopic machines are
not the microscopic equivalent of the macroscopic machines that we come across
in our daily life. We find that there is no one to one correspondence between
the performance of our system under engine protocol and its reverse.
