This paper proposes a novel dynamics model of the twisted and coiled polymer actuator (TCPA) which is one of the artificial muscles recently discovered. It can be driven by Joule heating and can contract up to 25%. Most of the conventional works employed the linear model of TCPA which represents the relationships between the input voltage, the temperature, and the displacement, but the real TCPA shows the nonlinearity. Although a nonlinear model was proposed based on the curve fitting, it is difficult to apply the model to the various TCPAs. Additionally, the conventional works cannot explain the effect of the convective heat transfer condition on the displacement behavior of TCPA. This paper aims to construct a general nonlinear model of TCPA based on the following two ideas: (1) The energy balance of TCPA and (2) the temperature and velocity dependence of the heat transfer coefficient. The temperature model is obtained from the time derivative of the energy balance, and the displacement model is derived as Lagrange's equation of motion with the dissipation function. Through experiments, it is verified that the proposed model is closer to the real dynamics than the conventional linear model.