Near-extremal black holes with an AdS2 throat are of great interest in string theory and in holography due to their ubiquity as classical gravitational saddles. The emergent SL(2,R) symmetry associated to the throat plays an important role in their low-temperature physics. In this talk, I will describe recent progress on analytically computing holographic correlators in black hole spacetimes with a near-extremal AdS2xR2 near-horizon geometry, focusing on current-current and shear correlators. By improving on previous matching calculations, I will show how it is possible to obtain analytical approximations to the correlators that interpolate between the hydrodynamic (frequencies small compared to the temperature) and the non-hydrodynamic low-temperature regimes. The expressions we obtain capture the hydrodynamic poles, the gapped poles controlled by the SL(2,R) symmetry of the AdS2 throat and the successive collisions with them. I will also comment on the appearance of zero temperature gapless poles in the spectrum and their relation to the SL(2,R) spectrum.