This thesis presents a study on the thermal transport through GaAs/AlAs superlattices (SLs). Compared to previous studies, we focus on SLs with the same total thickness and characterized not only the thermal conductivity, but also the SL structural properties. Molecular Beam Epitaxy (MBE) was used to fabricate four GaAs/AlAs SL samples, consisting of 5, 10, 42, and 100 periods, with each period consisting of 100/100 nm, 5/95 nm, 12/12 nm, 5/5 nm of GaAs/AlAs, respectively. Surface roughness and topography of the fabricated samples was measured by atomic force microscopy (AFM). The thicknesses of the GaAs and AlAs multilayers were estimated by X-ray diffraction (XRD). In order to prepare the samples for 3 measurements, atomic layer deposition (ALD) was utilized for the deposition of a thin insulating layer on the sample surface, while photolithography and metal evaporation were employed to create a metal strip with four contact pads. In the end, the cross-plane thermal conductivity of GaAs/AlAs SLs was measured in the temperature range from 250-310 K by employing the so-called "3 method". The thermal conductivity of the GaAs substrate was determined by the slope method, which gives a room temperature thermal conductivity of, consistent with literature data. Taking advantage of the differential 3 technique, the thickness dependency of GaAs/AlAs SLs is analyzed. In the mentioned temperature range, the thermal conductivity of GaAs/AlAs SLs increases with the increase in period thickness. The temperature-dependent measurements indicate that the thermal conductivity is constant (within the uncertainties) in the explored temperature range. This observation is ascribed to temperature-independent interface scattering strength combined with a weak temperature-dependence of the specific heat of the used materials. The obtained results may be used to validate computational models, which are being developed within the ongoing EU project "ALMA" (http://www.almabte.eu/).