Experimental tests investigating very-high-cycle fatigue (VHCF) properties of materials are commonly performed with ultrasonic testing machines, which allow for a significant reduction of testing time. In order to evaluate the effect of tested material volume (size-effect) on VHCF properties, the Authors recently proposed to adopt Gaussian specimens for VHCF tests. Investigation of size-effect with Gaussian specimen induces large mechanical power dissipation and temperature increment that must be taken into account. The present paper proposes an analytical model, which allows to approximately predict the dissipated mechanical power and the temperature increment in Gaussian specimens. The analytical model is also numerically verified through a Finite Element Analysis.