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There is paucity of literature on temperature generation in the reciprocating contacts. The objective of this paper is to demonstrate development of closed form solution for temperature rise at the non-lubricated piston ring/bore interface of the oil-less /oil-free air brake compressor. The solution will depend on parameters of reciprocating motion of the piston, gas load, piston ring geometry and thermophysical properties of the ring and bore material. The problem is reduced to solving the three-dimensional diffusion equation for a rectangular source of heat involved in a reciprocating motion. The solution is presented in an integral form. The temperature instabilities typical for a line source of heat are avoided by using a rectangular source of heat. The final results are obtained using numerical integration. Various cases of practical interest such as fast and slowly moving piston, long and short piston strokes are considered using a computer program.