We investigate the use of linear adaptation on Gaussian processes for Wi-Fi localization in a cross-device setting. We focus on the case where one has a training set collected with one or more devices and a very small labeled adaptation set from the test device. We first present an algorithm to find reliable linear fits between a training set and a small adaptation set by exploiting the Gaussian process assumption that all measurements are spatially correlated. Such regression algorithm is more reliable than total least squares when the adaptation set is very small. Second, we show that the regression misfit can be used to model the additional uncertainty in a linearly adapted map for cross-device Wi-Fi localization. When such uncertainty estimate is used to fuse Gaussian process maps created from one or more training sets and an adaptation set, localization performance can be greatly improved given just a few adaptation samples.