Based on the double exponential distributions of trap states in the channel of the hydrogenated amorphous silicon thin film transistor, characteristic temperatures of tail state and deep state are distinguished. Besides, series resistances are used to be associated with characteristic lengths of the source and the drain with trap states. By taking advantage of the Poisson equation and Gauss theorem, the expression of the threshold voltage distribution is obtained. The results show that with the increase of the distance between the point and the source, the threshold voltage decreases. Moreover, under the degradation of the self-heating effect, the distribution of the temperature in the channel is non-uniform and its variation in the channel center is the biggest.