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We study the back reaction of a thermal field in a weak gravitationalbackground depicting the far-field limit of a black hole enclosed in a box bythe Close Time Path (CTP) effective action and the influence functional method.We derive the noise and dissipation kernels of this system in terms ofquantities in quasi-equilibrium, and formally prove the existence of aFluctuation-Dissipation Relation (FDR) at all temperatures between the quantumfluctuations of the thermal radiance and the dissipation of the gravitationalfield. This dynamical self-consistent interplay between the quantum field andthe classical spacetime is, we believe, the correct way to treat back-reactionproblems. To emphasize this point we derive an Einstein-Langevin equation whichdescribes the non-equilibrium dynamics of the gravitational perturbations underthe influence of the thermal field. We show the connection between our methodand the linear response theory (LRT), and indicate how the functional methodcan provide more accurate results than prior derivations of FDRs via LRT in thetest-field, static conditions. This method is in principle useful for treatingfully non-equilibrium cases such as back reaction in black hole collapse.Comment: To appear in the proceedings of the Conference on Quantum Gravity in  the Southern Con

Fluctuations in a Thermal Field and Dissipation of a Black Hole Spacetime: Far-Field Limit