  We derive the asymptotic expansion of the heat kernel for a Laplace operator
acting on deformed spheres. We calculate the coefficients of the heat kernel
expansion on two- and three-dimensional deformed spheres as functions of
deformation parameters. We find that under some deformation the conformal
anomaly for free scalar fields on $R^4\times \tilde S^2$ and $R^6\times \tilde
S^2$ is canceled.
