Experimental tests investigating the gigacycle fatigue properties of materials are commonly performed with ultrasonic testing procedures, which allow for a significant reduction of testing time but induce a significant temperature increment in specimens. In order to evaluate the significance of size effects on the fatigue strength of materials, the Authors recently proposed to adopt Gaussian specimens for gigacycle tests. Fatigue specimens were designed without taking into account the hysteretic damping and its effects both on the stress distribution and on the heat power dissipation. However, in order to evaluate the temperature increment and the feasibility of ultrasonic fatigue tests with Gaussian specimens, the total dissipated heat power as well as the distribution of the dissipated heat power density along the specimen must be taken into account. The present paper proposes an analytical model validated through a finite element analysis, which permits to evaluate the effects of the hysteretic damping on the stress distribution, on the dissipated heat power density distribution and on the total dissipated heat power in Gaussian specimens. (C) 2014 Elsevier Ltd.