The 21 cm forest – H i absorption features in the spectra of high-redshift radio sources – can potentially provide a unique probe of the largely neutral intergalactic medium (IGM) during the epoch of reionization. We present semi-analytical models of the 21 cm forest due to the large-scale structure of the reionization-era IGM, including a prescription for X-ray heating and the percolation of photoionization bubbles. We explore a range of signal-analysis methods to show that, if detected with future instruments such as the Square Kilometre Array (SKA), the 21 cm forest can provide a significant constraint on the thermal history of the IGM. Detection will be aided by consideration of the sudden increase in signal variance at the onset of 21 cm absorption. If radio foregrounds and the intrinsic source spectra are well understood, the flux decrement over wide bandwidths can also improve detection prospects. Our analysis accounts for the possibility of narrow absorption lines from intervening dense regions, but, unlike previous studies, our results do not depend on their properties. Assuming X-ray heating corresponding to a local stellar population and a simple reionization model, we estimate that a statistically significant detection of 21 cm absorption could be made by the SKA in less than a year of observing against a Cygnus A-type source at z ∼ 9, as opposed to nearly a decade for a significant detection of the detailed forest features. We discuss observational challenges due to uncertainties regarding the abundance of background sources and the strength of the 21 cm absorption signal.