  We develop a semi-analytic method for assessing the impact of the large-scale
IGM temperature fluctuations expected following He${\rm\,{\scriptstyle II}}$
reionization on three-dimensional clustering measurements of the Ly$\alpha$
forest. Our methodology builds upon the existing large volume, mock Ly$\alpha$
forest survey simulations presented by Greig et al. by including a prescription
for a spatially inhomogeneous ionizing background, temperature fluctuations
induced by patchy He${\rm\,{\scriptstyle II}}$ photoheating and the clustering
of quasars. This approach enables us to achieve a dynamic range within our
semi-analytic model substantially larger than currently feasible with
computationally expensive, fully numerical simulations. The results agree well
with existing numerical simulations, with large-scale temperature fluctuations
introducing a scale-dependent increase in the spherically averaged 3D
Ly$\alpha$ forest power spectrum of up to 20-30 per cent at wavenumbers
$k\sim0.02$ Mpc$^{-1}$. Although these large-scale thermal fluctuations will
not substantially impact upon the recovery of the baryon acoustic oscillation
scale from existing and forthcoming dark energy spectroscopic surveys, any
complete forward modelling of the broad-band term in the Ly$\alpha$ correlation
function will none the less require their inclusion.
