The relationship between terrestrial deep soil temperature (TDST) and surface temperature (SAT) at interannual and centennial timescales has been investigated in a simulation of the last millennium with a three-dimensional climate model driven by estimations of historical external forcing. TDST is loosely related to borehole temperature profiles, which have been recently used to reconstruct long term temperature trends in the last centuries. Recently, questions about the validity of boreholes-based reconstructions have been raised. In the simulation, at interannual time scales the connection between TDST and SAT is stable, being stronger in the summer half year than in the winter half year. At long timescales, annual TDSL is a good proxy for annual SAT, and their variations are almost indistinguishable from each other. Both TDSL and terrestrial SAT overestimate the variations of global mean SAT. This may be a source for the disagreement between statistical reconstructions of global SAT and terrestrial borehole measurements.