  Continuum fitting uncertainties are a major source of error in estimates of
the temperature-density relation (usually parametrized as a power-law, $T
\propto \Delta^{\gamma - 1} $) of the inter-galactic medium (IGM) through the
flux probability distribution function (PDF) of the Lyman-$\alpha$ forest.
Using a simple order-of-magnitude calculation, we show that few percent-level
systematic errors in the placement of the quasar continuum due to e.g. a
uniform low-absorption Gunn-Peterson component, could lead to errors in
$\gamma$ of order unity. This is quantified further using a simple
semi-analytic model of the Lya forest flux PDF. We find that
under-(over-)estimates in the continuum level can lead to a lower (higher)
measured value of $\gamma$. Within current observational uncertainties,
continuum biases double the error in $\gamma$ from $\sigma_{\gamma} \approx
0.1$ to $\sigma_{\gamma} \approx 0.2$ within our model. We argue that steps
need to be taken to directly estimate the level of continuum bias in order to
make recent claims of an inverted \tdr\ more robust.
