To infer past climatic changes from temperatures measured in boreholes, one must obtain reliable estimates of ground surface temperature (GST) histories from these data. This paper presents a method that uses a Bayesian inverse technique to estimate the GST in the Fourier frequency domain. By assuming the a priori GST to be stationary, with a prescribed standard deviation and a cutoff period, the time series is constrained to be bounded and smooth. Because accounting for conductivity variations with depth is crucial to the estimatation of GST, a layered Earth medium has been used, for which the forward analytical solution of one-dimensional heat conduction is available. Borehole data from Flin Flon and Lac Dufault in Canada are inverted with this method. The Flin Flon hole, logged to a depth of 2900 m, provides an opportunity to study long-term GST variations, and the estimated GST from this hole shows some effects of deglaciation at the end of Pleistocene. At Lac Dufault, similar GSTs were obtained independently from three holes ranging from 550 to 900 m, and hence the results are considered more reliable. In the Lac Dufault GSTs, there is a warm period centered about 1000 years BP and a cold period about 400 years B.P., confirming the presence of the Little Climatic Optimum and the Little Ice Age, respectively. The Flin Flon result does not show the Little Climatic Optimum, and the Little Ice Age occurs about 100--200 years earlier. However, in both locations, the GSTs show another brief cold period around the turn of the century followed by rapid warming until 1940--1950, in good agreement with the trend of northern hemisphere surface air temperatures. ¿ American Geophysical Union 1992