We report on the modeling of electrical characteristics and contact-related effects of organic thin film transistors. An equivalent circuit is employed to simulate the electrical behavior of the devices. We suggest that, at low temperature, tunneling is the dominant mechanism of charge carrier injection, originating the nonlinearities often observed in these devices. The temperature dependence of the output characteristics is due to the fraction of carriers that are injected, via the competing mechanism of thermal activation, above the interface energy barrier at metal/organic contacts. The model successfully reproduces the electrical characteristics of P3HT polymeric transistors and allows for the decoupling and the study of the temperature dependence of the charge conduction through the organic channel.