In a recent experimental campaign, we used laser-accelerated relativistic hot electrons to ensure heating of thin titanium wire targets up to a warm dense matter (WDM) state EPL114, 45002 (2016)10.1209/0295-5075/114/45002. The WDM temperature profiles along several hundred microns of the wire were inferred by using spatially resolved X-ray emission spectroscopy looking at the Ti K characteristic lines. A maximum temperature of ∼30 eV was reached. Our study extends this work by discussing the influence of the laser parameters on temperature profiles and the optimisation of WDM wire-based generation. The depth of wire heating may reach several hundreds of microns and it is proven to be strictly dependent on the laser intensity. At the same time, it is quantitatively demonstrated that the maximum WDM temperature doesn't appear to be sensitive to the laser intensity and mainly depends on the deposited laser energy considering ranges of 6×10 -6×10 W/cm and 50-200 J.