Recent analyses of the intergalactic UV background by means of the He ii Ly \alpha forest assume that He ii and H i absorption features have the same line widths .
We omit this assumption to investigate possible effects of thermal line broadening on the inferred He ii /H i ratio \eta and to explore the potential of intergalactic He ii observations to constrain the thermal state of the intergalactic medium .
Deriving a simple relation between the column density and the temperature of an absorber based on the temperature-density relation T = T _ { 0 } ( 1 + \delta ) ^ { \gamma - 1 } we develop a procedure to fit T _ { 0 } , \gamma , and \eta simultaneously by modeling the observed spectra with Doppler profiles .
In an alternative approach the temperature T of an absorber , the He ii /H i ratio \eta , and the redshift scale of \eta variations are estimated simultaneously by optimizing the Doppler parameters of He ii .
Testing our procedure with artificial data shows that well-constrained results can be obtained only if the signal-to-noise ratio in the He ii forest is S / N \gtrsim 20 .
Additionally , ambiguities in the line profile decomposition may result in significant systematic errors .
Thus , it is impossible to give an estimate of the temperature-density relation with the He ii data available at present ( S / N \sim 5 ) .
However , we find that only 45 % of the lines in our sample favor turbulent line widths while the remaining lines are probably affected by thermal broadening .
Furthermore , the inferred \eta values are on average about 0.05 \mathrm { dex } larger if a thermal component is taken into account , and their distribution is 46 % narrower in comparison to a purely turbulent fit .
Therefore , variations of \eta on a 10 % level may be related to the presence of thermal line broadening .
The apparent correlation between the strength of the H i absorption and the \eta value , which has been found in former studies assuming turbulent line broadening , essentially disappears if thermal broadening is taken into account .
In the redshift range 2.58 < z < 2.74 towards the quasars HE~2347-4342 and HS~1700+6416 we obtain \eta \approx 100 and slightly larger .
In the same redshift range the far-UV spectrum of HS 1700+6416 is best and we estimate a mean value of \log \eta = 2.11 \pm 0.32 taking into account combined thermal and turbulent broadening .