Several different independent pieces of observational evidence suggest the tail-end of the HeII reionisation epoch occurred around z~3. It is expected this key milestone in the history of our Universe will have a significant impact on the thermal state of the IGM, boosting the IGM temperature and altering the polytropic temperature-density relation. I shall present new results, based on a comparison of detailed numerical simulations of the Lyman-alpha forest to high quality observational data, which suggest the temperature-density relation may be substantially more complex and the voids in the IGM are significantly hotter than is usually assumed at these redshifts. Radiative transfer effects which alter the spectral shape of ionising radiation during HeII reionisation provide one possible physical mechanism for inverting the IGM temperature-density relation. The implications of these results for the measurement of cosmological parameters from the Lyman-alpha forest flux power spectrum will also be briefly discussed.
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