Helium ion thermoluminescence (TL) fluence response is calculated as a function of particle energy from 1 to 10 MeV in the framework of the extended track interaction model (ETIM). The results of Monte Carlo calculations of absorbed dose as a function of the radial distance from the He ion track axis are employed for 1, 2, 2.6, 3.5, 4.95, 6.76 and 10 MeV He ions in condensed phase LiF. The radial dose is then transformed to radial occupation probabilities for the TL trapping and luminescent defect centres using optical absorption (OA) dose filling constants based on experimental gamma/electron OA dose response measurements. The radial defect occupation probabilities are used to estimate the track structure parameters (TSPs) r100 (full occupation defining the track core), r50 (50% occupation) and rh (track extension). These, of course, may be different for the trapping centres, luminescent centres and competitive centres due to their different charge carrier trapping cross-sections leading to different dose-filling constants. He ion TL fluence response (linearity, supralinearity and saturation) is then modelled in the framework of the ETIM with the TSPs and dose filling constants as input parameters. It is illustrated that the maximum supralinearity f(n)max increases smoothly with increasing particle energy due to the gradually increasing track radial extension and the increase in the number of electrons escaping the parent track, Ne, relative to the number recombining within the parent track, NW.