A series of experiments is conducted in which a variable solar irradiance is imposed for a range of frequencies and amplitudes in a simplified coupled General Circulation Model. For realistic amplitudes solar forcing dominates over internal variability in global mean surface air temperature (GM‐SAT) beyond decadal timescales. Its impact increases with period up to 50 years. Evidence is found for interactions between climate variations with different timescales. A weak 22‐yr solar irradiance variation excites a significant spectral peak with a 70‐yr period in GM‐SAT. On the regional‐scale the internal variability dominates at all timescales. Patterns of internal variability and their associated variance are robust for a variable solar forcing. The temporal spectra, however, are sensitive to such forcing. Some preferred decadal timescales of the internal modes of the coupled system disappear when the solar forcing varies.