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A new method for measuring, simultaneously or individually, the heat production rate, thermal diffusivity, and conductivity of solids accompanying internal heat production or consumption is presented. The method utilizes the principle of the Laplace transform and has the advantage of measuring the above variables under arbitrary heating or cooling conditions imposed on the samples as far as a unidirectional heat flow is concerned. The theory is developed for some practical measuring systems and verified by a numerical test and simple experiments.