In the context of climatic temperature studies, more often than not a time series is affected by artificial inhomogeneities. To overcome such limitation, we propose a new simple methodology in which promising results point not only toward the detection of unknown inhomogeneous periods but also toward the possibility of reconstructing the uncertain portion of the series. It is based on a parsimonious statistical downscaling (Multiple Linear Regression) of the large-scale 20CR reanalysis data. This method is successfully applied upon two long-range temperature series from a couple of centennial observatories (Ebre and Fabra, NE of Spain) which do not have nearby suitable temperature series to compare with. Results of trend analysis point to a clear signal of warming, with a larger rate of increase for the maximum temperature (respect to the minimum one), for the more recent decades (respect to the whole available period), and for the original series (respect to the reconstructed ones).