In this work, the design and development of a new variable linear power supply, using the LM317 regulator, is proposed. The originality of this power supply is related with the control of the rectifier circuit, which is based on a reference of voltage, superimposed on the output voltage. This reference is used in the control strategy to maintain a constant voltage between the input and the output voltages of the LM317 regulator. Due to this strategy, the heating losses are greatly reduced, allowing to increase the efficiency of the regulator to about 90%, and to reduce the requirements of the cooling system. Moreover, drawbacks of conventional power supplies are mitigated, where the developed variable linear power supply delivers a current of 3 A and a variable output voltage, from 1.2 V to 30 V. The LM317 regulator was modeled by its thermal equivalent structure associated with a heatsink to study the heat transfer problem. The modeling was performed on the Matlab Simulink software, and the theoretical results were validated by a set of experimental tests using the LM317 regulator.