In this paper, we construct a nonlinear reduced order model of a plasticization cylinder of injection machines, which has a spatially distributed nonlinear dynamics First, a distributed parameter model for the overall control system is derived based on the physical laws. Next, we attempt to reduce the model complexity focusing on the specific structure of the nonlinearity which arises from temperature-dependency of the rate of heat loss of heaters subjected to natural convection. This enables us to obtain a 28-dimensional model (via an 808-dimensional spatially discretized model) while theoretically guaranteeing a practically satisfactory accuracy. The obtained model is examined experimentally by using a prototype system.