Apparatus and method for cooling internal components of a down-hole well drilling apparatus. Components of the well drilling apparatus are encased in an inner canister that is further encased in an outer canister creating a void between the inner canister and the outer canister. Further, a plurality of moveable barriers is disposed between the inner canister and the outer canister and contains a heat transfer fluid. A plurality of agitators add mechanical energy to the plurality of moveable barriers compressing and expanding, while repositioning, the heat transfer fluid and creating a heat pump based on a reverse Stirling cycle to remove heat from the cooler inner canister and transfer the heat to the hotter environment outside the outer canister.