Increasingly advanced applications of polymer fibers are driving the demand for new, high-performance fiber types. One way to produce polymer fibers is by electrospinning from polymer solutions and melts. Polymer melt electrospinning produces fibers with small diameters through solvent-free processing and has applications within different fields, ranging from textile and construction, to the biotech and pharmaceutical industries. Modeling of the electrospinning process has been mainly limited to simulations of geometry-dependent electric field distributions. The associated large change in viscosity upon fiber formation and elongation is a key issue governing the electrospinning process, apart from other environmental factors. This paper investigates the melt electrospinning of aerogel-containing fibers and proposes a logistic viscosity model approach with parametric ramping in a finite element method (FEM) simulation. The formation of melt electrospun fibers is studied with regard to the spinning temperature and the distance to the collector. The formation of PET-Aerogel composite fibers by pneumatic transport is demonstrated, and the critical parameter is found to be the temperature of the gas phase. The experimental results form the basis for the electrospinning model, which is shown to reproduce the trend for the fiber diameter, both for polymer as well as polymer-aerogel composites.