We propose a scan test for the presence of spatial groupwise heteroskedasticity in cross-sectional data. The scan approach has been used in different fields before, including spatial econometric models, to detect instability in mean values of variables or regression residuals. In this paper, we extend its use to second order moments. Using large Monte Carlo simulations, we check the reliability of the proposed scan procedure to detect instabilities in the variance, the size and power of the test and its accuracy to find spatial clusters of observations with similar variances. Finally, we illustrate the usefulness of this test to improve the specification search in a spatial hedonic model, with an empirical application on housing prices in Madrid.