We have previously formulated a Bayesian approach to the Sampson and Guttorp model for the nonstationary correlation function r(x, x') of a Gaussian spatial process <Damian et al., 2001>. This model assumes that the nonstationarity can be encoded through a bijective space deformation, f, that defines a new coordinate system in which the spatial correlation function can be considered isotropic, namely r(x, x') = ρ(∥f(x) - f(x')∥), where ρ belongs to a known parametric family. We extend this model to incorporate spatial heterogeneity in site-specific temporal variances. In our Bayesian framework the variances are considered (hidden) realizations of another spatial process, which we model as log-Gaussian, with correlation structure expressed in terms of the same spatial deformation function underlying that of the observed process. We demonstrate the method in simulations and in an application.