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Continuum fitting uncertainties are a major source of error in estimates ofthe temperature-density relation (usually parametrized as a power-law, $T\propto \Delta^{\gamma - 1} $) of the inter-galactic medium (IGM) through theflux probability distribution function (PDF) of the Lyman-$\alpha$ forest.Using a simple order-of-magnitude calculation, we show that few percent-levelsystematic errors in the placement of the quasar continuum due to e.g. auniform low-absorption Gunn-Peterson component, could lead to errors in$\gamma$ of order unity. This is quantified further using a simplesemi-analytic model of the Lya forest flux PDF. We find thatunder-(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 $\sigma_{\gamma} \approx0.1$ to $\sigma_{\gamma} \approx 0.2$ within our model. We argue that stepsneed to be taken to directly estimate the level of continuum bias in order tomake recent claims of an inverted \tdr\ more robust.

Systematic Continuum Errors in the Lyman-Alpha Forest and The Measured Temperature-Density Relation