Based on Doppler-shift measurements we have determined the positron drift velocity u in a high-purity monoclinic \ensuremath{\alpha}-perylene single crystal as a function of applied electric field F and temperature. The electric field is applied as a triangular wave with a maximum field ${\mathit{F}}_{\mathrm{max}}$. At low fields the drift velocity displays a linear field dependence, while it assumes a sublinear field dependence above a characteristic velocity ${\mathit{v}}_{\mathit{s}}$=50 km/s and finally tends to saturate at 110 km/s, presumably due to optical-phonon generation above a certain threshold kinetic energy. Unlike in the case of diamond, ${\mathit{v}}_{\mathit{s}}$ is much greater than the longitudinal sound velocity in the solid. By fitting the observed nonlinear electric-field dependence of u to a Shockley expression for acoustic deformation potential scattering of ``warm'' charge carriers we extract the zero-field limit of the positron mobility ${\mathrm{\ensuremath{\mu}}}_{0}$ along the crystallographic c' axis (c'\ensuremath{\parallel}a\ifmmode\times\else\texttimes\fi{}b). At 297 K ${\mathrm{\ensuremath{\mu}}}_{0}$=(136\ifmmode\pm\else\textpm\fi{}3\ifmmode\pm\else\textpm\fi{}14) ${\mathrm{cm}}^{2}$ ${\mathrm{V}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, where the first error is statistical and the second is an estimated \ifmmode\pm\else\textpm\fi{}10% calibration uncertainty. Over the temperature range 100--350 K the mobility exhibits a ${\mathit{T}}^{\mathit{n}}$ temperature dependence with n=-1.04\ifmmode\pm\else\textpm\fi{}0.03, showing a clear departure from the ${\mathit{T}}^{\mathrm{\ensuremath{-}}3/2}$ dependence one might expect. Below 100 K ${\mathrm{\ensuremath{\mu}}}_{0}$ still increases with decreasing temperature, but at a given temperature its value decreases as the maximum applied field ${\mathit{F}}_{\mathrm{max}}$ increases, possibly indicating interference caused by the presence of a field-enhanced accumulation of trapped carriers that cause scattering at low temperatures.Below 50 K the limit of ${\mathrm{\ensuremath{\mu}}}_{0}$ as ${\mathit{F}}_{\mathrm{max}}$\ensuremath{\rightarrow}0 does not further increase but reaches a maximum value of \ensuremath{\approxeq}1000 ${\mathrm{cm}}^{2}$ ${\mathrm{V}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, an upper limit which is presumably set by the presence of residual impurities. These data will be compared with positron mobility results obtained for anthracene.