We study the corrected entropy due to thermal fluctuation and their effect on
the thermodynamics of a conformally dressed black hole in three dimensions. We
find that the thermal fluctuation affects the entropy significantly for small
black holes. Various corrected thermodynamical variables are also calculated
for this black hole. We observe that thermal fluctuation on the thermodynamics
of a small conformal black hole has a significant effect. We also analyse the
stability of black hole under the effect of thermal fluctuation. Due to thermal
fluctuation, instability occurs in the system of small conformal black holes.
Isothermal compressibility is also studied for this black hole which diverges
for the equilibrium state of the system.
