The results from an X-ray spectroscopic study of the giant elliptical galaxy NGC5044 in the center of a galaxy group are presented. The line dominated soft X-ray spectra (mainly Fe-L and O VIII Ly_a) from the diffuse gas are resolved for the first time in this system with the Reflection Grating Spectrometers on-board XMM-Newton and provide a strong constraint on the temperature structure. The spectra integrated over 2 (sim 20kpc) in full-width can be described by a two temperature plasma model of 0.7keV and 1.1keV. Most of the latter component is consistent with originating from off-center regions. Compared to the isobaric cooling flow prediction, the observation shows a clear cut-off below a temperature of 0.6 +-0.1keV. Furthermore, the Fe and O abundances within the central 10--20kpc in radius are accurately measured to be 0.55+-0.05 and 0.25+-0.1 times the solar ratios, respectively. The observed cut-off temperature of this galaxy and other central galaxies in galaxy groups and clusters are compared with the scale of the galaxy and properties of the surrounding intra-cluster medium. Based on this comparison, the origin of the lack of predicted cool emission is discussed.