This study investigates the influence of oceanic and atmospheric processes in extratropical thermodynamic air-sea interactions resolved by satellite observations (OBS) and by two climate model simulations run with eddy-resolving high-resolution (HR) and eddy-parameterized low-resolution (LR) ocean components. Here, spectral methods are used to characterize the sea surface temperature (SST) and turbulent heat flux (THF) variability and co-variability over scales between 50-10000 km and 60 days-80 years in the Pacific Ocean. The relative roles of the ocean and atmosphere are interpreted using a stochastic upper-ocean temperature evolution model forced by noise terms representing intrinsic variability in each medium, defined using climate model data to produce realistic rather than white spectral power density distributions. The analysis of all datasets shows that the atmosphere dominates the SST and THF variability over zonal wavelengths larger than ~2000-2500 km. In HR and OBS, ocean processes dominate the variability of both quantities at scales smaller than the atmospheric first internal Rossby radius of deformation (R1, ~600-2000 km) due to a substantial ocean forcing coinciding with a weaker atmospheric modulation of THF (and consequently of SST) than at larger scales. The ocean-driven variability also shows a surprising temporal persistence, from intraseasonal to multidecadal, reflecting a red spectrum response to ocean forcing similar to that induced by atmospheric forcing. Such features are virtually absent in LR due to a weaker ocean forcing relative to HR.