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This paper reports on the thermal field annealing effect of microwave permeabilities in CoFeHfO thin films. For the high resistive optimized Co19Fe53Hf8O20 thin films annealed at 150deg C, apart from excellent magnetic performance very low Gilbert damping constants (alpha < 0.017) are obtained up to film thickness of 437 nm. The results are interpreted in terms of changes in microstructure leading to structural relaxation effect and evolution of nanocrystalline Co(Fe) precipitates out of thermal field annealing. These materials with excellent low loss performance are obviously the most promising candidates for microwave device applications.