Excess heat often limits the lifetime or stability of semiconductor devices, like laser strcutures, e.g. by affecting the refractive index or defect formation. It is therefore vital to understand how thermal energy is dissipated from the active region. In this contribution, we analyze the in-plane thermal transport in GaN-based membranes which can be applied in UV-visible light emission. The temperature of the material is probed by the shift and width of Raman modes under heating with a UV laser. This method allows for a contactless characterization without the need for additional processing steps often needed for alternative thermometry. We find, that the thermal conductivity, κ, is significantly reduced compared to bulk GaN due to the finite thickness of the analyzed membranes. Phonon scattering due to roughness and porosity of the membrane is found to further reduce κ. Studying in-plane thermal transport lays the foundation for subsequent thermal studies on entire device structures; exploiting a subtle balance of in- and cross-plane thermal transport which could improve device designs