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In this work we present our recent results on the high-temperature plasma-assisted molecular beam epitaxy (PA-MBE) of hBN monolayers with atomically controlled thicknesses for 2D applications and on the growth of significantly thicker hBN layers for potential DUV applications. We also report our recent results on the high-temperature PA-MBE growth of hBN layers using a high-efficiency RF plasma source with high active nitrogen fluxes. Our results demonstrate that PA-MBE growth on highly oriented pyrolytic graphite (HOPG) substrates at temperatures ~1390°C can achieve mono- and few-layer thick hBN with a control of the hBN coverage and atomically flat hBN surfaces which is essential for 2D applications of hBN layers. The hBN monolayer coverage can be reproducible controlled by the PA-MBE growth temperature, time and B:N flux ratios. Significantly thicker hBN layers have been achieved at higher B:N flux ratios. We observed a gradual increase of the hBN thickness by decreasing the growth temperature from 1390°C to 1080°C. However, by decreasing the MBE growth temperature below 1250°C, we observe a rapid degradation of the optical properties of hBN layers. Therefore, high-temperature PA-MBE, above 1250°C, is a viable approach for the growth of high-quality hBN layers for 2D and DUV applications.