  We consider two families of exactly solvable models describing thermal
fluctuations in two-dimensional superconductors coupled to phonons living in an
insulating layer, and study the stability of the superconducting state with
respect to vortices. The two families are characterized by one or two
superconducting planes. The results suggest that the effective critical
temperature increases with the thickness of the insulating layer. Also the
presence of the additional superconducting layer has the same effect.
