To solve the problems of complex structure, poor reliability, and low intelligence of existing fan clutches for large hybrid vehicles, this paper proposes a new adaptive shape memory alloy intelligent fan clutch for large hybrid vehicle motor cooling. Based on the pure shear shape memory alloy thermodynamic effects, the relationship between shape memory alloy spring recovery force and temperature has been established; based on the shape memory alloy spring thermal drive characteristics and clutch construction dimensions, clutch torque transmission equations have been established. The shape memory alloy fan clutch transmission characteristics were quantitatively analyzed in terms of temperature, torque, rotational speed, and slip rate. The results show that the shape memory alloy fan clutch model based on the finite element method (FEM) and the established transmission model can accurately describe the mechanical characteristics of the shape memory alloy phase change process and the clutch torque transmission characteristics. When the clutch input speed is 3000 rad/min and the temperature is 100 °C, the output torque is 19.04 N·m, the speed is 2877.2 rad/min, and the slip rate is 4.3%. Due to the shape memory effect of shape memory alloy, the clutch can intelligently adjust the fan speed by sensing the ambient temperature. A fan clutch can satisfy the heat dissipation requirement of a large hybrid vehicle’s transmission system under complicated road conditions.