We present a detailed high spectral resolution ( R \sim 40000 ) study of five high-z damped Lyman \alpha systems ( DLAs ) and one sub-DLA detected along four QSO sightlines .
Four of these DLAs are very metal-poor with [ Fe/H ] \leq - 2 .
One of them , at z _ { abs } = 4.20287 towards J0953 - 0504 , is the most metal- poor DLA at z > 4 known till date .
This system shows no enhancement of C over Fe and O , and standard Population II star yields can explain its relative abundance pattern .
The DLA at z _ { abs } = 2.34006 towards J0035 - 0918 has been claimed to be the most carbon-enhanced metal-poor DLA .
However , we show that thermal broadening is dominant in this system and , when this effect is taken into account , the measured carbon enhancement ( [ C/Fe ] = 0.45 \pm 0.19 ) becomes \sim 10 times less than what was reported previously .
The gas temperature in this DLA is estimated to be in the range of 5000 - 8000 K , consistent with a warm neutral medium phase .
From photoionization modelling of two of the DLAs showing C ii * absorption , we find that the metagalactic background radiation alone is not sufficient to explain the observed C ii * cooling rate , and local heating sources , probably produced by in-situ star formation , are needed .
Cosmic ray heating is found to contribute \gtrsim 60 % to the total heating in these systems .
Using a sample of metal-poor DLAs with C ii * measurements , we conclude that the cosmic ray ionization rate is equal to or greater than that seen in the Milky Way in \sim 33 % of the systems with C ii * detections .