This letter offers new evidence motivating a more serious consideration of the potential Arctic temperature responses as a consequence of the decadal, multidecadal and longer-term persistent forcing by the ever-changing solar irradiance both in terms of total solar irradiance (TSI, i.e., integrated over all wavelengths) and the related UV irradiance. The support for such a solar modulator can be minimally derived from the large (>75%) explained variance for the decadally-smoothed Arctic surface air temperatures (SATs) by TSI and from the time-frequency structures of the TSI and Arctic SAT variability as examined by wavelet analyses. The reconstructed Arctic SAT time series based on the inverse wavelet transform, which includes decadal (5--15 years) and multidecadal (40--80 years) variations and a longer-term trend, contains nonstationary but persistent features that are highly correlated with the Sun's intrinsic magnetic variability especially on multidecadal time scales.