We compare the improved measurement of the Lya forest flux probability distribution at 1.7<z<3.2 presented by Kim et al. (2007) to a large set of hydrodynamical simulations of the Lya forest with different cosmological parameters and thermal histories. The simulations are in good agreement with the observational data if the temperature-density relation for the low density intergalactic medium (IGM), T=T_0 Delta^{gamma-1}, is either close to isothermal or inverted (gamma<1). Our results suggest that the voids in the IGM may be significantly hotter and the thermal state of the low density IGM may be substantially more complex than is usually assumed at these redshifts. We discuss radiative transfer effects which alter the spectral shape of ionising radiation during the epoch of HeII reionisation as a possible physical mechanism for achieving an inverted temperature-density relation at z~3.
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