Recent climatic records from the Greenland ice-core project (GRIP) ice core show that the climate proxy temperatures δ18O (18O/16O ratios) display sharp gradients and large fluctuations over all observed scales. We show that these variations are scale invariant over the range ≈400 yr to ≈40 kyr. The fluctuations corresponding to these scales are studied using multifractal analysis techniques. We estimate universal multifractal indices which characterize all the fluctuations for all the scales in this range and which are close to those obtained for turbulent temperatures at much shorter time scales. We speculate briefly on the origin of these common features intervening all over the observed range from seconds to kyr.