  We measure hole transport in poly(3-hexylthiophene) field effect transistors
with channel lengths from 3 $\mu$m down to 200 nm, from room temperature down
to 10 K. Near room temperature effective mobilities inferred from linear regime
transconductance are strongly dependent on temperature, gate voltage, and
source-drain voltage. As $T$ is reduced below 200 K and at high source-drain
bias, we find transport becomes highly nonlinear and is very strongly modulated
by the gate. We consider whether this nonlinear transport is contact limited or
a bulk process by examining the length dependence of linear conduction to
extract contact and channel contributions to the source-drain resistance. The
results indicate that these devices are bulk-limited at room temperature, and
remain so as the temperature is lowered. The nonlinear conduction is consistent
with a model of Poole-Frenkel-like hopping mechanism in the space-charge
limited current regime. Further analysis within this model reveals consistency
with a strongly energy dependent density of (localized) valence band states,
and a crossover from thermally activated to nonthermal hopping below 30 K.
