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In this paper we propose a localized regression technique to account forspatial non-stationarity in functional data relationships by generalising a geographical weighted regression model. We present an heteroskedastic version of the geographically weighted regression model for functional data which allows the residualvariance to vary across the space. In particular we propose to calibrate the variance of the model by replacing it by a continuous mean smoothing over the space. Inaddition, in order to deal with the calibration problem and to define and measure the so-called closeness in the spatial functional dimension, this paper proposes analternative back-fitting approach. Several simulation studies and an application onreal data show the performances of the proposed method.