High-energy decay channels of the Al Lyman-β satellite have been observed in X-ray emission from highly ionized plasma jets created by intense laser irradiation of aluminium foil targets. Atomic structure calculations show that the Lyman β satellite emission consists from six emission groups close to the He-like Al 1s2-1s4p (Heγ) and 1s2-1s5p (Heδ) resonance lines. This provides new possibilities for space resolved analysis of high density plasmas. Non-Maxwellian simulations of the plasma emission carried out with the MARIA code demonstrate that the intensity ratios of the Lyman-β satellites and the Heγ and Heδ resonance lines are very sensitive to the bulk electron temperature. In contrast to standard diagnostic methods, parameter studies show that this bulk electron diagnostics is practically unaffected by suprathermal electrons having less than 10 % of the bulk electron density.