It is necessary to use the low temperature thermal energy around 100 degress C from a viewpoint of global warming prevention. Even if a shape memory alloy is bent in normal temperature, when it is heated, it has the character which returns to the original straight form. Using this character of a shape memory alloy, unused thermal energy will be able to transform into rotation energy. A shape memory alloy belt is hung on a high temperature wheel and a low-temperature wheel. On this simple pulley type shape memory alloy engine, a shape memory alloy belt is heated with a high temperature wheel, it occurs a moment when returning to the original straight form, the moment kicks a high temperature wheel by the principle of action reaction, and torque is generated. We solved this torque generating mechanism. We proposed the theory which can design the output power of the simple pulley type shape memory alloy engine. Furthermore, the validity of this theory was verified by experiment.