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Recent analyses of the intergalactic UV background by means of the HeII Lymanalpha forest assume that HeII and HI absorption features have the same linewidths. We omit this assumption to investigate possible effects of thermal linebroadening on the inferred HeII/HI ratio eta and to explore the potential ofintergalactic HeII observations to constrain the thermal state of the IGM.Deriving a simple relation between the column density and the temperature of anabsorber we develop a procedure to fit the parameters of a power lawtemperature-density relation and eta simultaneously. In an alternative approachthe temperature of an absorber, eta, and the redshift scale of eta variationsare estimated simultaneously. Tests with artificial data show thatwell-constrained results can be obtained only if the signal-to-noise ratio inthe HeII forest is S/N > 20. Thus, it is impossible to give an estimate of thetemperature-density relation with the HeII data available at present (S/N ~5).However, we find that only 45% of the lines in our sample favor turbulent linewidths. Furthermore, the inferred eta values are on average about 0.05 dexlarger if a thermal component is taken into account, and their distribution is46% narrower in comparison to a purely turbulent fit. Therefore, variations ofeta on a 10% level may be related to the presence of thermal line broadening.The apparent correlation between the strength of the HI absorption and the etavalue, which has been found in former studies, essentially disappears ifthermal broadening is taken into account. In the redshift range 2.58 < z < 2.74towards the quasars HE2347-4342 and HS1700+6416 we obtain eta ~ 100. (abridged)Comment: accepted for publication by A&A, 11 pages, 13 figure

The HeII Lyman alpha forest and the thermal state of the IGM