NOVELTY - The system (100) has heat exchanger (104) that includes conduit (112) extended between inlet and outlet along length of heat exchanger. A packing fraction of fins (106) is increased from first packing fraction proximate the inlet to second packing fraction proximate the outlet. Each thermoelectric power generator is provided with thermoelectric element extended between hot and cold sides. The hot sides of power generators are in thermal contact with fins, such that temperature of each hot side is substantially equal along the length of heat exchanger.    USE - Thermoelectric power generating system using gradient heat exchanger.    ADVANTAGE - The thermoelectric conversion can be relied on the See-beck effect to convert temperature differences into electricity, so that the thermoelectric converters can be operated more efficiently under greater temperature differences. The thermoelectric power generation system can be enabled to use heat from heat source to provide a temperature difference across thermoelectric conversion elements so that the electricity is generated. The size and the spacing of the fins can be varied along the direction of fluid flow and/or in a direction transverse to fluid flow, so that relatively uniform temperature can be obtained at the hot sides of each module. The direct attachment of fins to the module cover can be enabled to eliminate the thermal interface problems between the heat exchanger and the thermoelectric generator module, so that the performance of the thermoelectric generator module can be significantly improved.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) thermoelectric power generation method;    (2) thermoelectric module; and    (3) method of generating electrical energy using thermoelectric module.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic cross sectional perspective view of power generating system.    Power generation system (100)    Thermoelectric power generator module (102)    Heat exchanger (104)    Fins (106)    Conduit (112)