The static path approximation to the nuclear partition function is app
lied within a canonical ensemble, utilizing the saddle-point approxima
tion for the finite temperature proton and neutron number projection.
Results obtained with a pairing plus quadrupole interaction indicate t
hat significant differences between the canonical and grand canonical
distribution over the deformation parameters and gaps may arise, parti
cularly in transitional nuclei like Dy-152. Comparison with effective
mean field approximations is also made.